Lithuanian trio Audrius Ksanavicius, Marius Zaliukas and Andrius Velicka all netted and when sub Christian Nade added a fourth in the 68th minute Falkirk must have feared the worst.
Yet it was John Hughes' side who threatened to pull off an amazing comeback with late goals from Graham Barrett and Pedro Moutinho but in the end they proved nothing more than consolation strikes.
Gorgie coach Stevie Frail was delighted to see his side earn another three points and was particularly pleased his Lithuanian players put on a show to answer their critics.
He said: "Someone highlighted last week that at one point we didn't have any in the side but three of them went out and scored today.
"However, as a club we don't look at them as Lithuanians, Spanish, Scottish or English.
"We look at them as Hearts players but it's good for them from a personal point of view that they can show people they want to play here and do well for the club."
Hearts got their noses in front in just six minutes with a brilliantly-worked passing move which ended in Ksanavicius opening his account for the season.
Eggert Jonsson's precise pass had released Laryea Kingston down the right and the midfielder's pinpoint cross found the Lithuanian unmarked inside the box and he slotted beyond Tim Krul.
The diminutive frontman was delighted with his goal. He said: "It was important to score my first goal. It's just a pity it's taken so long."
Ksanavicius - on loan from Kaunas - could have had a second after a good effort from long range midway through the first half but this time Krul saved.
Just before the half-hour, though, the home side did double their advantage and it was another Lithuanian who got on the score sheet to send Tynecastle wild.
Following a foul on Velicka on the edge of the box Michael Stewart floated in a free-kick. Darren Barr's headed clearance fell straight to Zaliukas and the stopper fired home a brilliant volley.
The first half was as comfortable as it gets for Hearts who were in cruise control and a minute before the hour mark things got even better with a third goal.
It was a Lithuanian combination down the left that did the damage with Tomas sending Velicka clear and the striker cut into the box before steering his shot past Krul.
There was little Hughes could do to stop the rot but he tried by making a triple substitution in the 65th minute - only for things to get worse-moments later when Hearts' own sub hit a fourth goal.
French striker Nade fired home after a one-two with Kingston only for referee Stuart Dougal to cut short his celebrations when he booked him for leaving the field of play to lap up the applause.
The Bairns looked dead and buried but to their credit they tried the impossible fightback and Barrett slotted home with three minutes left quickly followed by a cool side-foot finish from Moutinho.
Hearts keeper Steve Banks then had to get down low to scramble away another Barrett effort to ensure his side kept their two-goal cushion to kill off Falkirk's hopes.
MATCH STAT
HEARTS
SHOTS ON 9
SHOTS OFF 3
OFFSIDE 1
FOULS 5
CORNER 4
BOOKING 1
FALKIRK
SHOTS ON 8
SHOTS OFF 9
OFFSIDE 0
FOULS 3
CORNER 8
BOOKING 3
REF WATCH
STUART DOUGAL has admitted to his penalty blunder at Killie last week but no such problems here - a competent display.
