Falkirk 2 St. Mirren 0
Alan Gow came within inches of opening the scoring after five minutes when he curled a free-kick just wide of Chris Smith's left-hand post.
St Mirren responded and Billy Mehmet glanced a header wide from David van Zanten's cross.
The Bairns gained the upper hand not long afterwards. Russell Latapy picked out Moutinho, who turned John Potter, before firing a right-foot shot past Smith from 15 yards.
St Mirren tried to get back on terms but Falkirk were well-disciplined at the back and soaked up anything they could muster.
Van Zanten saw a shot blocked by Kenny Milne seven minutes before the break in their most promising raid as Falkirk defended solidly.
It was Falkirk that extended their lead two minutes later. Gow brilliantly controlled a long throughball from Darren Barr and then cut the ball back for O'Donnell to fire a terrific shot past Smith.
Early in the second half, Barr sent Moutinho scurrying clear but he chose to shoot early and Smith saved easily.
Richard Brittain had a chance to pull Saints back into it from a Craig Molloy cross but he volleyed tamely at Kasper Schmeichel.
It was Falkirk that looked like getting a third and Smith let a shot from substitute Liam Craig squirm through his fingers but he recovered to grab it on the line.