Steven Hammell had the game's first chance with a left-foot shot that drifted wide of the post.
Patrick Cregg then had a similar effort for the home side.
However, it was John Sutton who came closest in the first half as he headed over from inside the box.
Stevie May smashed wide when well placed, but the first half ended goalless.
However, with just five minutes gone in the second half May opened the scoring for the home side as he tapped in.
Motherwell had a few half-chances but soon found themselves 2-0 down. This time Nigel Hasselbaink found the bottom corner with a well struck shot.
Both May and Hasselbaink had further chances to increase the lead, but they were unable to find the target.