Dundee United had to play for the final 35 minutes with only ten men when striker Roy O'Donovan was red-carded for a two-footed challenge on Gerard Aafjes.
Falkirk pounded the United goal in the final minutes but could not get the break they needed and had to be content with a point.
United were first to threaten but it took them all of 20 minutes to get a clear sight of Falkirk's goal. O'Donovan knocked the ball on for strike partner Warren Feeney but his 18-yard shot sizzled high and wide.
Falkirk responded and Sean Dillon made a great blocking tackle to prevent Patrick Cregg from opening the scoring after Steve Lovell had set him up.
Gerard Aafjes then should have netted when Lukasz Zaluska spilled a low shot from Kevin McBride but he directed his shot at the goalkeeper.
The goalkeeper then had to get his angles right to close down a shot by O'Donovan after the ball had broken cruelly off Scott Arfield.
Burton O'Brien came close to one of his specials when he gathered the ball at the edge of the area after a flowing move instigated by Jackie McNamara, but he curled his left-foot shot just inches wide.
Zaluska was fortunate at the start of the second half when he failed to deal convincingly with a tame shot from Arfield but no Falkirk player was there to take advantage.
The goalkeeper did much better moments later when he managed to get his hand to a terrific strike from McNamara as United scrambled the ball away for a corner.
O'Donovan then received his marching orders after a rash challenge on Aafjes on the touchline that left referee Iain Brines with no dilemma.
Falkirk tried to make the numerical advantage count and McBride saw a 20-yard shot well saved by Zaluska.
But Craig Conway had a great chance to put United in front when Darren Barr missed his tackle, but he sent his shot into the side-netting.
Arfield created a shooting chance for Cregg at the other end when he robbed a loitering Paul Dixon, but the midfielder's shot was blocked and McBride sent the loose ball high over the top.
United held firm in the closing moments and kept Zaluska well protected to earn a point.