In a match that will not live long in the memory, neither side deserved to take three points but Falkirk finished the happier side.
Hearts started with midfielder Laryea Kingston deployed up front with Stephen Frail short of striking options.
A mistake by Kenny Milne gave Hearts an early chance but, as Calum Elliot bore down on goal, Darren Barr made the block to save his side.
Hearts suffered a setback when Deividas Cesnauskis had to go off with an injury after just 15 minutes which meant a reshuffle in their ranks.
It was an untidy game with neither goalkeeper particularly troubled in the first half-hour although the home side looked the more likely to make the breakthrough.
Scott Arfield had a rare effort on goal for Falkirk from distance but Steve Banks was relieved to see it flying yards wide of target.
Gerard Aafjes should have done better when he headed tamely wide after a decent cross from Tom Scobbie as Falkirk looked more threatening late in the first half.
Hearts wasted a good chance to go in front shortly before the break when substitute Andrius Ksanavicius saw a shot blocked by Barr before Michael Stewart lashed the loose ball wide.
Christophe Berra then headed over from a Kingston corner as Hearts pressed for the opener before half-time.
Milne should have given Falkirk the lead in the 58th minute when he had a free shooting chance on the edge of the area only to send his left-foot shot carelessly over the bar.
The game livened up in the closing stages with Falkirk substitute Pedro Moutinho making a difference when he came on.
Graham Barrett just failed to get on the end of a throughball from Arfield as the game became stretched.
Moutinho saw a late shot blocked before Scobbie rushed his follow-up shot well wide as Hearts breathed a sigh of relief.
The home side left the field to a chorus of boos and their chances of making the top-six now look increasingly slim.