The home side dominated the opening stages of the match and could have been 3-0 up inside 10 minutes but for some spectacular reflex saves by Falkirk goalkeeper Matt Glennon.
Hearts' pressure eventually paid off on 20 minutes when Paul Hartley came out on top in a goalmouth scramble and slotted his right-footed shot into the net from close range.
Stephen O'Donnell piled the pressure on Falkirk three minutes later when he was sent off after picking up a second yellow card for a poor challenge on Andy Webster.
Three minutes later Hearts made their one-man advantage tell as they doubled their lead. This time it was Rudi Skacel who netted, notching up his 14th goal of the season with an unstoppable left-foot shot from the edge of the area, which sped past Glennon.
The Bairns held their own and Russell Latapy and Darryl Duffy both produced half chances for the visitors, but a third Hearts goal just before the break put paid to Falkirk's five-match unbeaten SPL record.
It was Calum Elliot who netted his first goal for the Tynecastle side four minutes before the interval, bundling the ball in from two-yards after a defensive error.
Substitute Michal Pospisil continued the rout on 73 minutes with a diving header after a well-timed cross from Robbie Neilson.
Elliot completed a memorable day by scoring his second of the day in injury-time, swerving a right-footed shot low into the net.
The confidence-boosting result puts Hearts seven points clear of third-place Hibs going into their crucial New Year's Day clash against SPL leaders Celtic.