Islam Chesnokov's first goal for Hearts picked up three precious points in a hard-fought encounter at Tynecastle Park.
The Kazakhstan international tucked away a classy finish from close range right at the first half's conclusion and, despite several more chances at both ends of the pitch, the men in maroon held on to claim another vital victory after last week's defeat at Rangers.
Derek McInnes made two tweaks to the side that was beaten at Ibrox last time out; Tomas Magnusson replacing the injured Beni Baningime, whilst Michael Steinwender came in for the similarly stricker Oisin McEntee.
The Bairns carved out the first half-chance after four minutes, with a tidy backheel opening the door for Brad Spencer to have a dig from distance, his effort eventually trickling well wide of Alex Schwolow's post.
Falkirk enjoyed a huge slice of luck to prevent Hearts' opener after 14 minutes, Leon McCann accidentally nodding the ball back towards his own net after Alexandros Kyziridis smashed an inviting ball across the face of goal, but Scott Bain reacted quickly to halt it's advance.
Hearts had a chance of their own after ten minutes as Claudio Braga made good headway down the right before cutting back to a waiting Blair Spittal, but his effort deflected behind from his vicious snapshot at Bain.
The pendulum continued to swing, and Falkirk got another half-chance away at Schwolow, with Barney Stewart's effort from close range held by the German as the Jambos repelled their assault.
If not for the offside flag, Islam Chesnokov helped craft a fine move heading towards the half-hour mark, latching onto Braga's knock-down before going on goal - shanking his attempt high and wide as Bain raced out to meet the Kazakhstan international.
Falkirk carved out another chance on the counter as game ticked towards the final five, cutting out a Magnusson ball before driving up the pitch; Keelan Adams sliding across to Benjamin Broggio who fired high and wide over the crossbar.
With just a minute to go until the break, Hearts finally broke the deadlock, with Islam Chesnokov opening his account in a maroon jersey.
From a sweeping move that saw Milne thread into Kyziridis, the Greek winger unselfishly laid the ball into the path of Chesnokov, who tucked the ball away underneath the helpless figure of Bain.
HT: Heart of Midlothian 1-0 Falkirk
Just ten seconds into the restart and Hearts had a chance to double their lead, Braga screwing wide from inside the box after good work by Tomas Magnusson to work the ball into his path.
Scott Bain was on hand to deny Hearts another goal after 74 minutes, throwing himself to the right to beat away a Braga shot from close range that seemed destined for the back of the Bairns net.
With ten minutes to go, it very much remained an open contest, but Hearts were able to keep pressuring Bain as full-time approached, with the Falkirk 'keeper producing another fine save as Kyziridis cut inside and beat two men before curling at goal.
In the first minute of added time, Kyziridis went close once again, forcing Bain into a tipped save over the bar from his blistering free-kick 25-yards from goal.
The Jambos held on though, and remain top of the league ahead of next week's meeting with Aberdeen at Tynecastle Park.
Hearts: Schwolow, Halkett, Braga, Steinwender (Altena 81'), Milne, Findlay (McCart 84'), Magnusson (Kabore 81'), Spittal, Leonard, Kyziridis, Chesnokov
Subs: Fulton, Kent, McCart, Kabore, Kabangu, Forrest, Altena, Kerjota, Mato
Falkirk: Bain, Adams, McCann, Donaldson (Allan 73'), Spencer (Cartwright 73'), Broggio (Williams 73'), Stewart, Tait, Wilson (Marsh 50'), Lissah, Miller (Ross 73')
Subs: Hogarth, Graham, Yeats, Cartwright, Allan, Ross, Williams, Marsh, Hart
Attendance: 18,820
