Falkirk now sit two minutes behind the Tynecastle men with two matches remaining.
There was a low-key beginning to the game with h sides displaying typical end of season lethargy and it took no less than 24 minutes before a serious attempt at goal was unleashed.
The visitors were the aggressors on this occasion, Laryea Kingston collecting a superbly weighted crossfield pass from Calum Elliott and advancing on goal, before firing in a strong angular shot which was turned round the post by Bairns keeper Shane Supple.
From the resultant corner taken by Kingston, Christophe Berra again tested Supple, the Irishman saving well from the Hearts defender's header.
Falkirk's first threat on the Hearts goal occurred on the half hour when Pedro Moutinho took advantage of a slack pass by Ruben Palazuelos, the Portuguese frontman shooting wide of Steve Banks' right-hand post.
It was the home side who finished the first half the stronger and they took the lead in the first minute of injury time, young defender Tam Scobbie volleying past Banks from Moutinho's corner .
Inspired by Scobbie's strike - it was the first time Falkirk had scored in front of their own supporters since mid February - the Bairns began the second half aggressively with Carl Finnigan attempting to release the well positioned Michael Higdon, who was denied by an excellent blocking tackle from Jose Goncalves.
Falkirk were pushing hard to increase their lead, an objective they achieved in the 52nd minute when Finnigan finished off a brilliant passing movement involving Patrick Cregg and man of the match Scobbie, heading past Banks from close range to make it 2-0.
The Bairns were looking particularly comfortable at this stage and the collective frustration of the Hearts players became increasingly apparent, with Jamie Mole being yellow carded by referee Stuart Dougal for a foul in the 71st minute and Deividas Cesnauskis suffering a similar fate shortly afterwards, the Lithuanian having been adjudged to have dived in an attempt to win a penalty.
Cesnauskis redeemed himself to some extent 13 minutes from time with a fine individual goal but, despite some late pressure from Hearts, Falkirk held on for victory.