The home side looked to have started well as they forced a number of corners in the early minutes.
But it was Falkirk who almost opened the scoring after only four minutes, when hesitancy in the Well defence allowed Daniel McBreen acres of space, but Colin Meldrum saved brilliantly from the striker's angled drive.
After an open start to the game the match went a bit stale with neither side causing any problems in front of goal.
But the stalemate was broken in the thirt30thieth minute when keeper Allan Ferguson could only parry Jim Hamilton's volley from the edge of the box. Unfortunately for the keeper Scott McDonald was on hand to waltz round him and tap the ball into the empty net.
The second half had an all-action start with Motherwell scoring two early on with McDonald bending an 18-yarder past the helpless Ferguson.
Richie Foran repeated the feat minutes later but this time his bending shot was from a far more acute angle.
The visitors responded well and pulled one back on 54 when Patrick Cregg's low drive bounced in off the far post, despite the linesman's flag being raised the ref had a word and let the goal stand.
Falkirk applied pressure for much of the remainder of the half without really testing Meldurm in the home goal, with only another Cregg drive causing any problems as it slid past the post.