After closest rivals Rangers were held to a 1-1 draw by Alloa earlier in the day, Hearts seized the opportunity to go six points clear thanks to first-half goals from Kevin McHattie and Soufian El Hassnaoui.
Spurred on by a large travelling contingent of Jambos fans at the Falkirk Stadium, the leaders made the brighter start with El Hassnaoui in the thick of the action.
The Dutch-born Moroccan narrowly missed the target with a header from Billy King’s inviting cross, and he was denied by Jamie MacDonald’s reaction save at the near post after latching onto Prince Buaben’s through-ball.
El Hassnaoui had another effort deflected wide after Buaben had fired into the side-netting before Hearts deservedly broke the deadlock in the 27th minute.
A flowing move resulted in King feeding McHattie, who cut into the left side of the box and defied a difficult angle to drill beyond MacDonald and into the corner.
MacDonald got his angles right to keep out King’s near-post effort moments later, but the home keeper was powerless to stop Hearts doubling their lead on 37 minutes when El Hassnaoui swept in Jamie Walker’s drive across the face of goal.
Former Hearts player David Smith curled a free-kick wide for the home side, who improved after the break as Alex Cooper’s well-struck 25 yarder forced Neil Alexander into his first save.
Alexander pulled off another smart stop to thwart Cooper again, and the Hearts goalkeeper also dealt with David McCracken’s downward header from close range.
MacDonald kept the Bairns in the game with a fine save from Walker before Falkirk pulled a goal back in the 71st minute, when Botti Biabi was allowed space and time in the box to rifle a low shot across Alexander and into the far corner.
James Keatings should have made the game safe when he collected Walker’s pass and missed the target from barely six yards.
Falkirk piled on the pressure in the closing stages, but the well-organised Hearts backline held out to record their 11th win in 13 league games this season.