Both sides contributed to an end to end encounter but it seemed things were going the home side's way when they took the lead in the 26th minute and Hearts were reduced to ten men.
Russell Latapy played a superb ball behind the visiting defence to Darryl Duffy and when the striker nipped past Craig Gordon the big keeper caught his ankle.
Gordon was red-carded and Duffy himself gave stand-in keeper Steve Banks no chance from the spot.
The magnificent Latapy almost made it 2-0 nine minutes later when he dribbled to the edge of the box before driving a low left-foot shot that Banks did well to grab on the line.
Hearts' woes continued shortly after when Julien Brellier went off injured and when John Hughes' side scored their second goal in the 67th minute it looked all over.
A Duffy shot was blocked by Banks' chest, and although Pressley looked to have the rebound covered, the ball rebounded off his knee and trundled over the line.
Four minutes later however the league leaders rekindled some hope when Pressley was left unmarked at the right post to direct a Paul Hartley free-kick into the net.
Just when the home fans were ready to celebrate a shock victory, the Jambos skipper was on hand six yards out to prod the ball over the line after Matt Glennon had blocked Deividas Cesnauskis' close-range header.
The excitement was not finished however and Falkirk almost won the game when Pedro Moutinho dribbled into the box two minutes into stoppage-time but his left-foot shot flew inches over the bar.