If Edinburgh rivals Hibernian fail to beat Rangers on Sunday, Hearts will be in an unassailable position.
Osman Sow set up Jamie Walker for the opening goal, with the midfielder lashing home a shot from 10 yards.
Genero Zeefuik added the second after the interval with a powerful strike and substitute James Keatings found the top corner late on.
Falkirk are the only side to beat Hearts in the league this season, having enjoyed a 3-2 success at Tynecastle in January.
Peter Houston's side were also unbeaten in their last 11 games but the hosts were no match for the runaway leaders.
All eyes on Edinburgh on Sunday.