Falkirk also hit woodwork twice but a draw was a fair result as St Mirren looked to have things well in control after Billy Mehmet netted.
Marc Twaddle had a great chance to put Falkirk ahead after only four minutes when he was left unguarded at a Russell Latapy corner. But, from just six yards out, he failed to get any power or direction on his header and Tony Bullock was untroubled.
Sutton almost got in behind the Falkirk defence when Scott Higgins failed to come from a long clearance from Tony Bullock but again Barr was alert to the danger.
But it was Falkirk who came close to the breakthrough after 18 minutes. Jack Ross headed the ball into the path of Steven Thomson and the Falkirk skipper's 20-yard shot was touched onto the crossbar by Bullock for a magnificent save.
It was a rare effort on goal in a first half where Falkirk had the bulk of possession but were too pedestrian and predictable.
Richard Brittain tested Higgins midway through the half when he was given too much time to latch onto a Sutton cutback but the goalkeeper saved comfortably.
Alan Gow had a superb chance to give Falkirk the lead after a lay-off from Pedro Moutinho 12 minutes from the break but he shot tamely at Bullock from 16 yards.
Brittain wasted a chance at the tail end of the first half when the ball broke to him in the area but he curled his shot over the top.
But it was Falkirk who took control at the start of the second half.
Gow shot straight at Bullock when he should have done better and then Thomson hit woodwork again. He looked to have done everything right when he met a Jack Ross cross
with his head but the ball struck the post.
Mehmet opened the scoring after 69 minutes when he slammed home a low shot after Sutton knocked the ball into his path.
But Falkirk finished strongly. Stokes got his reward for a hard shift as he tucked home the equaliser. Kevin McGowne was lucky referee Willie Collum was unsighted as he tugged John Stewart back as he homed in on goal.