Hearts led through a first-half goal from Ruben Palazuelos, but Falkirk came back strongly in the second half to send the Edinburgh side to their fifth straight defeat.
Hearts started brightly and Ibrahim Tall saw an early shot blocked after Falkirk failed to deal with a cross from Michael Stewart after a short free-kick.
But it was Falkirk who fashioned the first chance after 13 minutes when Tom Scobbie's free-kick was not cleared and the ball broke to Dean Holden, but Steve Banks managed to block the ball for a corner.
Holden was allowed a free header at the corner but it bounced tamely into the arms of Banks.
Stewart won the ball to set up a shooting chance for Calum Elliot and his crisply-struck shot from 20 yards slipped wide of Tim Krul's right-hand post.
Andrew Driver managed to get in behind the Falkirk defence but the angle was too tight and he could only send a hopeful shot across the face of the goal.
Hearts were clearly in the mood and moments later a great run from Lee Wallace ripped the Falkirk defence apart and it took a tremendous save from Krul to divert the ball for a corner.
Falkirk managed to clear the flag-kick as far as Driver and his cross was headed in by Palazuelos, who had made a great break into the box.
The scorer was booked as he left the field to celebrate with fans behind goal but his exuberance could be excused given the wretched run Hearts had endured.
It was the breakthrough Hearts had craved. Elliot then pounced on some slack defensive play from Falkirk but could only fire a shot across goal which found no takers.
Kestutis Ivaskevicius should have extended Hearts' lead nine minutes from the break when the ball broke to him 15 yards out but he lacked composure and sent his shot wide.
Falkirk had a half-hearted shot for a penalty before half-time when a 25-yard shot from Steven Thomson appeared to strike Christophe Berra's arm, but the Hearts skipper knew little about it.
Substitute Carl Finnigan equalised for Falkirk after 78 minutes when he prodded the ball home from close range after a Pedro Moutinho corner broke to him.
Russell Latapy then combined with Finnigan to set up Higdon and he cracked an unstoppable shot past Banks for the winner.