<PAGE>   1
                                                                    EXHIBIT 10.1

                     FIRST AMENDMENT TO EMPLOYMENT AGREEMENT

         THIS FIRST AMENDMENT TO EMPLOYMENT AGREEMENT (this "FIRST AMENDMENT")
dated as of March 8, 2001 (the "AMENDMENT EFFECTIVE DATE") by and between The
Houston Exploration Company, a Delaware corporation (the "COMPANY"), and Thomas
W. Powers (the "EXECUTIVE").

                                   WITNESSETH:

         WHEREAS, the Company and the Executive entered into an Employment
Agreement dated as of July 2, 1996 (the "AGREEMENT") with an Effective Date of
September 19, 1996; and

         WHEREAS, the Company and the Executive hereby desire to amend the
Agreement as set forth herein;

         NOW, THEREFORE, in consideration of the premises and for other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the Company and the Executive hereby agree as follows:

         1. The Agreement shall be amended to reflect that the Executive's
position with the Company shall be that of Senior Vice President, Chief
Financial Officer and Treasurer.

         2. The Agreement shall be amended by adding the following provisions to
the end of Section 1:

                  The Executive agrees to continue his employment with the
                  Company notwithstanding the retirement of James G. Floyd as
                  President and Chief Executive Officer of the Company for at
                  least the period of time described in the next sentence (and
                  potentially thereafter). This period of continued employment
                  shall begin on the Amendment Effective Date and expire on
                  April 1, 2002. On April 1, 2002, the Executive shall have
                  thirty (30) days within which to provide the Company with a
                  Notice of Termination pursuant to Section 7 hereof. If the
                  Executive provides the Company with a Notice of Termination
                  within this period, the Executive shall be entitled to all
                  payments, additional compensation and benefits (including, but
                  not limited to, the payment described in Section 7(e) of 2.99
                  times Total Compensation, and vesting of stock options and
                  phantom stock) described in this Agreement as if a Change of
                  Control had occurred (whether or not a Change of Control
                  actually occurred or has occurred at such date) upon the
                  effective date specified in the Notice of Termination, such
                  effective date to be not more than ninety (90) days after the
                  date of the Notice of Termination). If the Executive does not
                  provide a Notice of Termination within the thirty (30) day
                  period, the Executive's employment with the Company shall
                  continue and this Agreement shall remain in full force and
                  effect according to its terms.

         3. Effective as of April 1, 2001, the Agreement shall be amended by
changing the salary per year referenced in Section 3 from "$140,000 per year" to
"$250,000 per year."

         4. The Agreement shall be amended by deleting the language in Section
7(e) after paragraph (iii) thereof in the definition of the term "Good Reason"
continued in subparts (G)(1)_(4), which formerly required that certain events
also occur before a Change of Control would constitute Good Reason and trigger
the lump sum severance payments provided in Section 7(e). As amended, subpart
(G) of the definition of Good Reason now reads in its entirety as follows:

                           (G)      the occurrence of a Change of Control.

         5. The Agreement shall be amended by modifying the second sentence of
Section 6(a) to provide that the termination of the Agreement will also
terminate the non-compete provisions contained therein. As amended, Section 6(a)
now reads in its entirety as follows:



<PAGE>   2

                  (a)      Noncompetition Activities. The Executive acknowledges
                           that the nature of the employment under this
                           Agreement is such as will bring the Executive in
                           personal contact with patrons or customers of the
                           Company and will enable him to acquire valuable
                           information as to the nature and character of the
                           business of the Company, thereby enabling him, by
                           engaging in the competing business on his own behalf,
                           or for another, to take advantage of such knowledge
                           and thereby gain an unfair advantage. Accordingly,
                           the Executive covenants and agrees that he will not,
                           without the prior written consent of the Company
                           during the Term of Employment, engage directly or
                           indirectly for himself, or as an agent,
                           representative, officer, director or employee of
                           others, in the exploration for or production of
                           hydrocarbons in waters offshore from the States of
                           Texas and Louisiana, provided that the foregoing
                           restriction shall not apply at any time after the
                           Executive's Term of Employment and, provided further,
                           that nothing in this Agreement shall prohibit the
                           Executive from acquiring or holding any issue of
                           stock or securities of any entity registered under
                           Section 12 of the Securities and Exchange Act of 1934
                           (as amended), listed on a national securities
                           exchange or quoted on the automated quotation system
                           of the National Association of Securities Dealers,
                           Inc., so long as the Executive is not deemed to be an
                           "affiliate" of such entity, as such term is used in
                           paragraphs (c) and (d) of Rule 145 under the
                           Securities Act of 1933 (as amended).

         6. The Agreement shall be amended to clarify the scope of the term
"total compensation" in Section 7(e). Section 7(e)(i) shall be amended to read
in its entirety as follows:

                  (i)      pay to the Executive, within thirty (30) days after
                           the date of such termination, a lump sum payment
                           equal to 2.99 times the Executive's then-current
                           annual rate of Total Compensation;

The following provision shall be added to the end of Section 7(e):

         As used in this Agreement, the term "Total Compensation" shall mean the
sum of the following:

                  (i)      the current annual salary of the Executive referenced
                           in Section 3;

                  (ii)     the current car allowance provided by the Company to
                           the Executive referenced in Section 4(c); and

                  (iii)    the Executive's annual bonus, calculated as though
                           the Company's financial targets had been met at one
                           hundred percent (100%) referenced in Section 3 and
                           Exhibit A hereto.

         7. Exhibit A to the Agreement shall be amended by changing the
"Percentage of Salary for Target Annual Bonus" for the Executive from 45% to
55%.

         8. The Agreement shall be amended by modifying the last sentence of
Section 14 to read in its entirety as follows:

                           This Agreement, as amended by the First Amendment,
                           constitutes the sole agreement between the parties
                           with respect to the employment of the Executive by
                           the Company and supersedes any and all other
                           agreements, oral or written, between the parties.



                                      -2-
<PAGE>   3

         9. Except as expressly amended hereby, the Company and the Executive
ratify and confirm all terms and conditions of the Agreement as continuing in
full force and effect.

         IN WITNESS WHEREOF, the parties hereto have duly executed this First
Amendment as of the date first above written.

                                  THE HOUSTON EXPLORATION COMPANY
Addresses:


                                       By: /s/ Robert B. Catell
                                          --------------------------------------
1100 Louisiana, Suite 2000             Name: Robert B. Catell
Houston, Texas 77002                   Title: Chairman, Compensation Committee



                                       By: /s/ Thomas W. Powers
                                          --------------------------------------
1100 Louisiana, Suite 2000                Thomas W. Powers
Houston, Texas 77002



                                      -3-