<PAGE>

                                                                   EXHIBIT 10.18

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AND HAVE BEEN ACQUIRED FOR INVESTMENT AND NOT WITH A
VIEW TO, OR IN CONNECTION WITH, THE SALE OR DISTRIBUTION THEREOF. NO SUCH SALE
OR DISTRIBUTION MAY BE EFFECTED WITHOUT AN EFFECTIVE REGISTRATION STATEMENT
RELATED THERETO OR AN OPINION OF COUNSEL IN A FORM SATISFACTORY TO THE COMPANY
THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF 1933.
--------------------------------------------------------------------------------

Warrant No. CS-1                             Number of Shares:  1,000,000
Date of Issuance:  April 14, 2000            (subject to adjustment)

                              DURECT CORPORATION

     Durect Corporation (the "Company"), for value received, hereby certifies
                              -------
that ALZA Corporation, or its registered assigns (the "Registered Holder"), is
                                                       -----------------
entitled, subject to the terms set forth below, to purchase from the Company,
commencing on the date the warrant is first exercisable in accordance with
Section 1(a) below until the Expiration Date (as defined in Section 5 below), up
to 1,000,000 shares (as adjusted from time to time pursuant to the provisions of
this Warrant) of Common Stock of the Company, at a purchase price (the "Purchase
                                                                        --------
Price") equal to $7.00 per share; provided, however, that prior to the time when
-----
the Warrant shall first become exercisable in accordance with Section 1(a), each
time, if any, that the Company sells equity securities in a private placement
transaction or series of related transactions in which the aggregate value of
securities sold exceeds $2,000,000 and in which the price per share of such
securities on an as converted basis (the "Sale Price") is greater than $7.00,
then the Purchase Price shall be adjusted so as to equal the Sale Price, and
provided further that in the event the Warrant shall first become exercisable
under Section 1(a) as a result of the completion by the Company of a registered
offering under the Securities Act of 1933, as amended, then the Purchase Price
shall equal the price per share at which the Company's Common Stock is offered
to the public in such offering.  The Purchase Price shall be subject to further
adjustment as set forth below.  The shares purchasable upon exercise of this
Warrant, as adjusted from time to time pursuant to the provisions of this
Warrant, are sometimes hereinafter referred to as the "Warrant Stock."
                                                       --------------

     1.   Exercise.
          --------

          (a)  Ability to Exercise. This Warrant shall be first exercisable on
               -------------------
the date that is the earlier of: (i) October 14, 2001, (ii) the date on which
the Company completes a registered offering under the Securities Act of 1933, as
amended, or (iii) the date on which the Company completes the sale, conveyance
or disposal of all or substantially all of the Company's property or business or
the Company's merger into or consolidation with any other corporation (other
than a wholly-owned subsidiary of the Company) or any other transaction or
series of related transactions in which more than fifty percent (50%) of the
voting power of the Company is disposed of, provided that this sub-Section
                                            --------
1(a)(iii) shall not apply to a merger effected exclusively for the purpose of
changing the domicile of the Company.

                                      -1-
<PAGE>

          (b)  Manner of Exercise.  This Warrant may be exercised by the
               ------------------
Registered Holder, in whole or in part, by surrendering this Warrant, with the
purchase/exercise form appended hereto as Exhibit A duly executed by such
                                          ---------
Registered Holder or by such Registered Holder's duly authorized attorney, at
the principal office of the Company, or at such other office or agency as the
Company may designate, accompanied by payment in full of the Purchase Price
payable in respect of the number of shares of Warrant Stock purchased upon such
exercise.  The Purchase Price may be paid by cash, check, wire transfer or by
the surrender of promissory notes or other instruments representing indebtedness
of the Company to the Registered Holder.

          (c)  Effective Time of Exercise.  Each exercise of this Warrant shall
               --------------------------
be deemed to have been effected immediately prior to the close of business on
the day on which this Warrant shall have been surrendered to the Company as
provided in Section 1(b) above.  At such time, the person or persons in whose
name or names any certificates for Warrant Stock shall be issuable upon such
exercise as provided in Section 1(e) below shall be deemed to have become the
holder or holders of record of the Warrant Stock represented by such
certificates.

          (d)  Net Issue Exercise.
               ------------------

               (i)    In lieu of exercising this Warrant in the manner provided
above in Section 1(b), the Registered Holder may elect to receive shares equal
to the value of this Warrant (or the portion thereof being canceled) by
surrender of this Warrant at the principal office of the Company together with
notice of such election on the purchase/exercise form appended hereto as Exhibit
                                                                         -------
A duly executed by such Registered Holder or such Registered Holder's duly
-
authorized attorney, in which event the Company shall issue to holder a number
of shares of Common Stock computed using the following formula:

                      X =  Y (A - B)
                           ---------
                                A
Where     X = The number of shares of Common Stock to be issued to the
               Registered Holder.

          Y = The number of shares of Common Stock purchasable under this
               Warrant (at the date of such calculation).

          A = The fair market value of one share of Common Stock (at the date of
               such calculation).

          B = The Purchase Price (as adjusted to the date of such calculation).

               (ii)   For purposes of this Section 1(d), the fair market value
of one share of Common Stock on the date of calculation shall mean:

                      (A)  if the exercise is in connection with an initial
public offering of the Company's Common Stock, and if the Company's Registration
Statement relating to such public offering has been declared effective by the
Securities and Exchange Commission, then the

                                      -2-
<PAGE>

fair market value per share of Common Stock shall be the initial "Price to
Public" specified in the final prospectus with respect to the offering;

                    (B)  if this Warrant is exercised after, and not in
connection with, the Company's initial public offering, and if the Company's
Common Stock is traded on a securities exchange or The Nasdaq Stock Market or
actively traded over-the-counter:

                         (1)  if the Company's Common Stock is traded on a
securities exchange or The Nasdaq Stock Market, the fair market value shall be
deemed to be the average of the closing prices over a thirty (30) day period
ending three days before date of calculation, or since the shares were first
traded on such exchange, if less than thirty three (33) days; or

                         (2)  if the Company's Common Stock is actively traded
over-the-counter, the fair market value shall be deemed to be the average of the
closing bid or sales price (whichever is applicable) over the thirty (30) day
period ending three days before the date of calculation, or since the shares
were first traded on such exchange, if less than thirty three (33) days; or

                    (C)  if neither (A) nor (B) is applicable, the fair market
value shall be at the highest price per share which the Company could obtain on
the date of calculation from a willing buyer (not a current employee or
director) for shares of Common Stock sold by the Company, from authorized but
unissued shares, as reasonably determined in good faith by the Board of
Directors, unless the Company is at such time subject to a transaction as
described in Section 1(a)(iii) above, in which case the fair market value per
share of Common Stock shall be deemed to be the value of the consideration per
share received by the holders of such stock pursuant to such transaction.

          (e)  Delivery to Holder.  As soon as practicable after the exercise of
               ------------------
this Warrant in whole or in part, and in any event within ten (10) days
thereafter, the Company at its expense will cause to be issued in the name of,
and delivered to, the Registered Holder, or as such Holder (upon payment by such
Holder of any applicable transfer taxes) may direct:

               (i)  a certificate or certificates for the number of shares of
Warrant Stock to which such Registered Holder shall be entitled, and

               (ii) in case such exercise is in part only, a new warrant or
warrants (dated the date hereof) and in the same form as this warrant, calling
in the aggregate on the face or faces thereof for the number of shares of
Warrant Stock equal (without giving effect to any adjustment therein) to the
number of such shares called for on the face of this Warrant minus the number of
such shares purchased by the Registered Holder upon such exercise as provided in
Section 1(b) above.

     2.   Adjustments.
          -----------

          (a)  Stock Splits and Dividends.  If outstanding shares of the
               --------------------------
Company's Common Stock shall be subdivided into a greater number of shares or a
dividend in Common

                                      -3-
<PAGE>

Stock shall be paid in respect of Common Stock, the Purchase Price in effect
immediately prior to such subdivision or at the record date of such dividend
shall simultaneously with the effectiveness of such subdivision or immediately
after the record date of such dividend be proportionately reduced. If
outstanding shares of Common Stock shall be combined into a smaller number of
shares, the Purchase Price in effect immediately prior to such combination
shall, simultaneously with the effectiveness of such combination, be
proportionately increased. When any adjustment is required to be made in the
Purchase Price, the number of shares of Warrant Stock purchasable upon the
exercise of this Warrant shall be changed to the number determined by dividing
(i) an amount equal to the number of shares issuable upon the exercise of this
Warrant immediately prior to such adjustment, multiplied by the Purchase Price
in effect immediately prior to such adjustment, by (ii) the Purchase Price in
effect immediately after such adjustment.

          (b)  Reclassification, Etc.  In case of any reclassification or change
               ----------------------
of the outstanding securities of the Company or of any reorganization of the
Company (or any other corporation the stock or securities of which are at the
time receivable upon the exercise of this Warrant) or any similar corporate
reorganization on or after the date hereof, then and in each such case the
holder of this Warrant, upon the exercise hereof at any time after the
consummation of such reclassification, change, reorganization, merger or
conveyance, shall be entitled to receive, in lieu of the stock or other
securities and property receivable upon the exercise hereof prior to such
consummation, the stock or other securities or property to which such holder
would have been entitled upon such consummation if such holder had exercised
this Warrant immediately prior thereto, all subject to further adjustment as
provided in Section 2(a); and in each such case, the terms of this Section 2
shall be applicable to the shares of stock or other securities properly
receivable upon the exercise of this Warrant after such consummation.

          (c)  Adjustment Certificate.  When any adjustment is required to be
               ----------------------
made in the Warrant Stock or the Purchase Price pursuant to this Section 2, the
Company shall promptly mail to the Registered Holder a certificate setting forth
(i) a brief statement of the facts requiring such adjustment, (ii) the Purchase
Price after such adjustment and (iii) the kind and amount of stock or other
securities or property into which this Warrant shall be exercisable after such
adjustment.

     3.   Transfers.
          ---------

          (a)  Unregistered Security.  Each holder of this Warrant acknowledges
               ---------------------
that this Warrant and the Warrant Stock have not been registered under the
Securities Act of 1933, as amended (the "Securities Act"), and agrees not to
                                         --------------
sell, pledge, distribute, offer for sale, transfer or otherwise dispose of this
Warrant or any Warrant Stock issued upon its exercise in the absence of (i) an
effective registration statement under the Act as to this Warrant or such
Warrant Stock and registration or qualification of this Warrant or such Warrant
Stock under any applicable U.S. federal or state securities law then in effect
or (ii) an opinion of counsel, reasonably satisfactory to the Company, that such
registration and qualification are not required.  Each certificate or other
instrument for Warrant Stock issued upon the exercise of this Warrant shall bear
a legend substantially to the foregoing effect.

                                      -4-
<PAGE>

          (b)  Transferability. Subject to the provisions of Section 3(a) hereof
               ---------------
and of Section 1.14 of the Second Amended and Restated Investors' Rights
Agreement dated March 28, 2000 among the Company and certain holders of the
Company's securities, this Warrant and all rights hereunder are transferable, in
whole or in part, upon surrender of the Warrant with a properly executed
assignment (in the form of Exhibit B hereto) at the principal office of the
                           ---------
Company; provided, however, that this Warrant may not be transferred to any
         --------  -------
party whom the Company reasonably determines is a competitor of the Company.

          (c)  Warrant Register.   The Company will maintain a register
               ----------------
containing the names and addresses of the Registered Holders of this Warrant.
Until any transfer of this Warrant is made in the warrant register, the Company
may treat the Registered Holder of this Warrant as the absolute owner hereof for
all purposes; provided, however, that if this Warrant is properly assigned in
              --------  -------
blank, the Company may (but shall not be required to) treat the bearer hereof as
the absolute owner hereof for all purposes, notwithstanding any notice to the
contrary.  Any Registered Holder may change such Registered Holder's address as
shown on the warrant register by written notice to the Company requesting such
change.

     4.   No Impairment.  The Company will not, by amendment of its charter or
          -------------
through reorganization, consolidation, merger, dissolution, sale of assets or
any other voluntary action, avoid or seek to avoid the observance or performance
of any of the terms of this Warrant, but will (subject to Section 13 below) at
all times in good faith assist in the carrying out of all such terms and in the
taking of all such action as may be necessary or appropriate in order to protect
the rights of the holder of this Warrant against impairment.

     5.   Termination.  This Warrant (and the right to purchase securities upon
          -----------
exercise hereof) shall terminate upon the date (the "Expiration Date") that is
                                                     ---------------
the fourth anniversary after the Warrant first becomes exercisable in accordance
with Section 1(a) above.

     6.   Notices of Certain Transactions.  In case:
          -------------------------------

          (a)  the Company shall take a record of the holders of its Common
Stock (or other stock or securities at the time deliverable upon the exercise of
this Warrant) for the purpose of entitling or enabling them to receive any
dividend or other distribution, or to receive any right to subscribe for or
purchase any shares of stock of any class or any other securities, or to receive
any other right, to subscribe for or purchase any shares of stock of any class
or any other securities, or to receive any other right, or

          (b)  of any capital reorganization of the Company, any
reclassification of the capital stock of the Company, any consolidation or
merger of the Company, any consolidation or merger of the Company with or into
another corporation (other than a consolidation or merger in which the Company
is the surviving entity), or any transfer of all or substantially all of the
assets of the Company, or

          (c)  of the voluntary or involuntary dissolution, liquidation or
winding-up of the Company,

                                      -5-
<PAGE>

then, and in each such case, the Company will mail or cause to be mailed to the
Registered Holder of this Warrant a notice specifying, as the case may be, (i)
the date on which a record is to be taken for the purpose of such dividend,
distribution or right, and stating the amount and character of such dividend,
distribution or right, or (ii) the effective date on which such reorganization,
reclassification, consolidation, merger, transfer, dissolution, liquidation or
winding-up is to take place, and the time, if any is to be fixed, as of which
the holders of record of Common Stock (or such other stock or securities at the
time deliverable upon such reorganization, reclassification, consolidation,
merger, transfer, dissolution, liquidation or winding-up) are to be determined.
Such notice shall be mailed at least ten (10) days prior to the record date or
effective date for the event specified in such notice.

     7.   Reservation of Stock.  The Company will at all times reserve and keep
          --------------------
available, solely for the issuance and delivery upon the exercise of this
Warrant, such shares of Warrant Stock and other stock, securities and property,
as from time to time shall be issuable upon the exercise of this Warrant.

     8.   Exchange of Warrants.  Upon the surrender by the Registered Holder of
          --------------------
any Warrant or Warrants, properly endorsed, to the Company at the principal
office of the Company, the Company will, subject to the provisions of Section 3
hereof, issue and deliver to or upon the order of such Holder, at the Company's
expense, a new Warrant or Warrants of like tenor, in the name of such Registered
Holder or as such Registered Holder (upon payment by such Registered Holder of
any applicable transfer taxes) may direct, calling in the aggregate on the face
or faces thereof for the number of shares of Common Stock called for on the face
or faces of the Warrant or Warrants so surrendered.

     9.   Replacement of Warrants.  Upon receipt of evidence reasonably
          -----------------------
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and (in the case of loss, theft or destruction) upon delivery of an
indemnity agreement (with surety if reasonably required) in an amount reasonably
satisfactory to the Company, or (in the case of mutilation) upon surrender and
cancellation of this Warrant, the Company will issue, in lieu thereof, a new
Warrant of like tenor.

     10.  Notices.  Any notice required or permitted by this Warrant shall be in
          -------
writing and shall be deemed sufficient upon receipt, when delivered personally
or by courier, overnight delivery service or confirmed facsimile, or forty-eight
(48) hours after being deposited in the regular mail as certified or registered
mail (airmail if sent internationally) with postage prepaid, addressed (a) if to
the Registered Holder, to the address of the Registered Holder most recently
furnished in writing to the Company and (b) if to the Company, to the address
set forth below or subsequently modified by written notice to the Registered
Holder.

     11.  No Rights as Stockholder.  Until the exercise of this Warrant, the
          ------------------------
Registered Holder of this Warrant shall not have or exercise any rights by
virtue hereof as a stockholder of the Company.

     12.  Registration Rights.  The Company covenants that it will amend that
          --------------------
certain Second Amended and Restated Investors' Rights Agreement dated March 28,
2000 to include the

                                      -6-
<PAGE>

shares of Common Stock issuable upon exercise of this Warrant as "Registrable
Securities" as defined in Section 1.1(b) of said agreement so that such shares
of Common Stock shall have the same registration rights under the Rights
Agreement as with respect to shares of the Company's Series A-1 Preferred Stock
held by the Registered Holder. If such amendment is not completed within 30 days
after the date of this Warrant, then the Warrant Stock shall not be subject to
the Amended and Restated Market Stand-Off Agreement dated June 19, 1998.

     13.  No Fractional Shares.  No fractional shares of Common Stock will be
          --------------------
issued in connection with any exercise hereunder.  In lieu of any fractional
shares which would otherwise be issuable, the Company shall pay cash equal to
the product of such fraction multiplied by the fair market value of one share of
Common Stock on the date of exercise, as determined in good faith by the
Company's Board of Directors.

     14.  Amendment or Waiver.  Any term of this Warrant may be amended or
          -------------------
waived only by an instrument in writing signed by the party against which
enforcement of the amendment or waiver is sought.

     15.  Headings.  The headings in this Warrant are for purposes of reference
          --------
only and shall not limit or otherwise affect the meaning of any provision of
this Warrant.

     16.  Governing Law. This Warrant shall be governed, construed and
          -------------
interpreted in accordance with the laws of the State of California, without
giving effect to principles of conflicts of law.



                              DURECT CORPORATION


                              By:  /s/ James E. Brown
                                   _____________________________________
                                   James E. Brown, President

                              Address:   10240 Bubb Road
                                         Cupertino, CA  95014

                                      -7-
<PAGE>

                                   EXHIBIT A
                                   ---------

                            PURCHASE/EXERCISE FORM
                            ----------------------

To:  DURECT CORPORATION                       Dated:

     The undersigned, pursuant to the provisions set forth in the attached
Warrant No. CS-1, hereby irrevocably elects to (a) purchase _____ shares of the
Common Stock covered by such Warrant and herewith makes payment of $ _________,
representing the full purchase price for such shares at the price per share
provided for in such Warrant, or (b) exercise such Warrant for _______ shares
purchasable under the Warrant pursuant to the Net Issue Exercise provisions of
Section 1(c) of such Warrant.

     The undersigned acknowledges that:

     A.   The Warrant Stock to be acquired by the undersigned will be acquired
for investment for the undersigned's own account, not as a nominee or agent, and
not with a view to the resale or distribution of any part thereof, and that the
undersigned has no present intention of selling, granting any participation in,
or otherwise distributing the same.  By executing this form, the undersigned
further represents that the undersigned does not presently have any contract,
undertaking, agreement or arrangement with any person to sell, transfer or grant
participations to such person or to any third person, with respect to any of the
Warrant Stock. The undersigned has not been formed for the specific purpose of
acquiring the Warrant Stock.

     B.   The undersigned understands that the Warrant Stock has not been, and
will not be, registered under the Securities Act, by reason of a specific
exemption from the registration provisions of the Securities Act which depends
upon, among other things, the bona fide nature of the investment intent and the
accuracy of the undersigned's representations as expressed herein.  The
undersigned understands that the Warrant Stock is "restricted securities" under
applicable U.S. federal and state securities laws and that, pursuant to these
laws, the undersigned must hold the Warrant Stock indefinitely unless they are
registered with the Securities and Exchange Commission and qualified by state
authorities, or an exemption from such registration and qualification
requirements is available.  Except as set forth in the Second Amended and
Restated Investors' Rights Agreement dated March 28, 2000, as amended, the
undersigned acknowledges that the Company has no obligation to register or
qualify the Warrant Stock for resale.  The undersigned further acknowledges that
if an exemption from registration or qualification is available, it may be
conditioned on various requirements including, but not limited to, the time and
manner of sale, the holding period for the Warrant Stock, and on requirements
relating to the Company which are outside of the undersigned's control, and
which the Company is under no obligation and may not be able to satisfy.

     C.   The undersigned understands that the Warrant Stock and any securities
issued in respect of or exchange for the Warrant Stock, may bear one or all of
the following legends:

          (a)  "THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AND HAVE BEEN

                                      -i-
<PAGE>

ACQUIRED FOR INVESTMENT AND NOT WITH A VIEW TO, OR IN CONNECTION WITH, THE SALE
OR DISTRIBUTION THEREOF. NO SUCH SALE OR DISTRIBUTION MAY BE EFFECTED WITHOUT AN
EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL IN A
FORM SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED UNDER
THE SECURITIES ACT OF 1933."

          (b)  Any legend required by the Blue Sky laws of any state to the
extent such laws are applicable to the shares represented by the certificate so
legended.

     D.   The undersigned is an accredited investor as defined in Rule 501(a) of
Regulation D promulgated under the Securities Act.

     E.   The undersigned further acknowledges that it has reviewed the market
standoff provisions set forth in Section 1.14 of the Second Amended and Restated
Investors' Rights Agreement dated March 28, 2000 among the Company and certain
holders of the Company's securities and agrees to be bound by such provisions.
In addition to the foregoing restrictions, and subject to Section 12 of the
Warrant, the undersigned further agrees that the Warrant Stock is also subject
to the terms of that certain Amended and Restated Market Stand-Off Agreement
entered into by and between the Company and Purchaser dated June 19, 1998, and
for the purposes of such agreement, the undersigned shall be deemed to hold the
Warrant Stock as of the date of the Warrant.





                                        Signature: ______________________

                                        Name (print): ___________________

                                        Title (if applic.): _____________

                                        Company (if applic.): ___________

                                     -ii-
<PAGE>

                                   EXHIBIT B

                                ASSIGNMENT FORM

     FOR VALUE RECEIVED, _________________________________________ hereby sells,
assigns and transfers all of the rights of the undersigned under the attached
Warrant with respect to the number of shares of Common Stock covered thereby set
forth below, to:

                                      -3-