They took nearly an hour to score against a team four levels of the Scottish game below them.
Marvin Johnson thought eased their nerves, Scott McDonald headed a second.
And Chris Cadden added a late third when he slotted in Richard Tait's cut-back.
James McFadden, who once upon a time looked anything but future officer material, was making his debut as Motherwell assistant manager to replace Stephen Robinson, who moved to become manager of Oldham Athletic.
He helped oversee a stuttering performance in the summer drizzle by his team who desperately needed all three points if they had any plans to finish second in the group F behind Rangers.
It was all Motherwell from the start and Johnson - with a dazzling solo run - and Scott McDonald - with a lob - Chris Cadden, Ben Heneghan and Johnson again, could all have scored.
However, despite the relentless pressure they couldn't get the ball in the net in the first half.
It was remarkable, but the 'Shire - despite being swamped - held out and actually threatened with one shot of their own, from Derek Ure.
Fans of the home side and neutral observers would reflect that it couldn't go on like this, and neither it did.
Just eight minutes into the second half, Johnson, the outstanding player on the park, gave the Premiership side the lead with a turn and a low left foot shot from just inside the box.
McDonald added a second to calm the home support in a crowd of 2,503 and minutes before the final whistle Chris Cadden made it 3-0 against a now weary 'Shire to keep their team alive in the battle to finish second in the group.
Match ends, Motherwell 3, East Stirling 0.
Second Half ends, Motherwell 3, East Stirling 0.
Attempt saved. Marvin Johnson (Motherwell) right footed shot from outside the box is saved in the bottom right corner.
Goal!  Motherwell 3, East Stirling 0. Chris Cadden (Motherwell) right footed shot from the centre of the box to the bottom left corner. Assisted by Richard Tait.
Attempt missed. Craig Comrie (East Stirling) right footed shot from outside the box misses to the right.
Corner,  Motherwell. Conceded by Connor Greene.
Attempt saved. Lionel Ainsworth (Motherwell) right footed shot from outside the box is saved in the bottom right corner.
Attempt missed. Lionel Ainsworth (Motherwell) right footed shot from the right side of the six yard box is just a bit too high.
Substitution, East Stirling. Lewis Peddie replaces Dylan McGuigan.
Attempt blocked. Chris Cadden (Motherwell) right footed shot from the centre of the box is blocked.
Foul by Craig Clay (Motherwell).
Paul Sludden (East Stirling) wins a free kick on the right wing.
Foul by Ben Heneghan (Motherwell).
David Grant (East Stirling) wins a free kick in the defensive half.
Goal!  Motherwell 2, East Stirling 0. Scott McDonald (Motherwell) header from very close range to the top right corner. Assisted by Chris Cadden.
Substitution, East Stirling. Craig Comrie replaces Conor Hogg.
Attempt saved. Joe Chalmers (Motherwell) right footed shot from outside the box is saved in the top centre of the goal.
Corner,  Motherwell. Conceded by Andy Grant.
Substitution, East Stirling. Paul Sludden replaces Adam Murray.
Attempt missed. David Grant (East Stirling) left footed shot from outside the box is close, but misses to the right.
Attempt missed. Lionel Ainsworth (Motherwell) right footed shot from outside the box misses to the left.
Attempt blocked. Craig Clay (Motherwell) left footed shot from the centre of the box is blocked.
Corner,  Motherwell. Conceded by Connor Greene.
Attempt missed. Stephen McManus (Motherwell) right footed shot from the centre of the box misses to the right.
Corner,  Motherwell. Conceded by Ross Fisher.
Attempt blocked. Lionel Ainsworth (Motherwell) right footed shot from a difficult angle and long range on the left is blocked.
Corner,  Motherwell. Conceded by Darren Dolan.
Keith Lasley (Motherwell) wins a free kick in the defensive half.
Foul by Kristopher Faulds (East Stirling).
Corner,  Motherwell. Conceded by Connor Greene.
Attempt blocked. Marvin Johnson (Motherwell) right footed shot from the left side of the box is blocked.
Attempt saved. Derek Ure (East Stirling) right footed shot from outside the box is saved in the bottom left corner.
Corner,  East Stirling. Conceded by Joe Chalmers.
Substitution, Motherwell. Joe Chalmers replaces Steven Hammell.
Substitution, Motherwell. Lionel Ainsworth replaces Dom Thomas.
Goal!  Motherwell 1, East Stirling 0. Marvin Johnson (Motherwell) left footed shot from the centre of the box to the bottom right corner. Assisted by Craig Clay.
Foul by Dom Thomas (Motherwell).
Kristopher Faulds (East Stirling) wins a free kick on the left wing.
Attempt saved. Marvin Johnson (Motherwell) header from the centre of the box is saved in the bottom right corner.
Second Half begins Motherwell 0, East Stirling 0.
Motherwell feasted on possession against East Stirlingshire but made a meal of scoring goals in their Betfred League Cup tie against the Lowland League side.