A goal from Edgaras Jankauskas nine minutes from time maintained Hearts' quest for second place in the SPL.
Jankauskas (right) is congratulated by team-mates
The visitors took the lead when Paul Hartley slotted home Rudi Skacel's cross from close range.
Falkirk were level on the stroke of half-time when Alan Gow forced the ball home at the second attempt, after Craig Gordon had saved his spot-kick.
Hearts restored their lead when Jankauskas forced in a Calum Elliot pass from six yards.
Hearts did not appear to be affected by the midweek events as they threatened the Falkirk goal early on.
Debutante Mark Howard could only push Hartley's long-range strike into the danger area where Skacel was following up but the goalkeeper did well to turn his powerful 16-yard shot away.
Steven Pressley was off the pitch receiving treatment when Falkirk carved out a glorious opportunity to take the lead shortly after.
Liam Craig swung a great ball towards the edge of six-yard box but Tiago Rodrigues sent a glancing header inches past the far upright.
However, Hearts made Falkirk pay as Skacel found a burst of pace to go past Jack Ross and centre where Hartley arrived to steer the ball past Howard from seven yards out in the 22nd minute.
Referee Alan Freeland sparked controversy when he awarded Falkirk a penalty in the final minute of the half.
He adjudged Roman Bednar to have handled Gow's free-kick and pointed to the spot.
Gow stepped up himself and, although Craig Gordon made a great save, the Bairns striker followed up to force the ball into the roof of the net.
Hearts lost Pressley at the break - which was a concern with next week's Scottish Cup semi-final against Hibernian in mind - and he was replaced by Christophe Berra.
The game came to life in the 54th minute, with both sides facing up to each other after some full-blooded challenges from Falkirk.
Julien Brellier went down theatrically under a Twaddle tackle, the latter yellow-carded as the referee struggled to keep control.
The midfielder sought retribution and lunged at Craig with a shocking challenge which also saw his name taken.
However, Hearts snatched the lead again in the 81st minute when Elliot slipped the ball through to Jankauskas.
And, somehow, the Lithuanian international forced the ball past on-loan Howard and into the far corner of the net.
Falkirk: Howard, Ross, Twaddle (McPherson 88), Rodrigues, Lescinel, Cregg, Thomson, Craig (O'Donnell 85), Dodds, Moutinho (Latapy 70), Gow. Subs Not Used: Hill, Lawrie, Theobold, Lima.
Booked: Twaddle, Craig, Moutinho, Cregg.
Goals: Gow 45.
Hearts: Gordon, Neilson (Petras 82), Fyssas, Pressley (Berra 50), Goncalves, Brellier, Cesnauskis, Hartley, Skacel (Elliot 64), Jankauskas, Bednar. Subs Not Used: Banks, Camazzola, Mikoliunas, Aguiar.
Booked: Pressley, Neilson, Brellier, Jankauskas.
Goals: Hartley 22, Jankauskas 81.
Ref: A Freeland