A 73rd-minute strike from substitute Roman Bednar broke the stalemate and gave Hearts all three points in a tense battle with 10-man Falkirk.
The Czech striker finished off a move created by fellow substitutes Ibrahim Tall and Andrew Driver.
Falkirk could not find a way back into a Bank of Scotland Premier League match which ended in furious scenes after Darren Barr saw red for a seemingly innocuous clash with Andrius Velicka.
The Lithuanian crashed to the ground after the players squared up following a foul on Barr, but referee Steve Conroy saw fit to dismiss the Falkirk youngster.
Scotland goalkeeper Craig Gordon was a surprise omission from the Hearts team.
He was the subject of a rejected £2.5million bid from English Premiership outfit Fulham this week.
Hearts stated that Gordon was suffering from a groin strain.
That was the main talking point of a poor game until Bednar's goal sparked the match to life.
Paul Hartley came close in the 19th minute after seizing possession 30 yards out, only for Kasper Schmeichel to throw himself low to his right to block, in the first real chance.
And three minutes later, Falkirk should have taken the lead.
Russell Latapy's corner was headed goalwards by Cedric Uras and when goalkeeper Steve Banks saved on the line Barr somehow managed to head wide off the post from three yards out.
The Bairns, who lined up in a 4-5-1 formation with Alan Gow on his own up front, slowly took a grip of possession and the Tynecastle side struggled to string any meaningful passing moves together.
They finally managed to show some creativity on the half-hour mark as Neil McCann, struggling to find any options, picked out Andrius Velicka wide on the left.
The Lithuanian powered in from the touchline and struck a shot which goalkeeper Schmeichel did well to block.
There were appeals for a penalty as Saulius Mikoliunas jumped with Karl Dodd for the rebound but the only result was an injury to the Falkirk defender, resulting in him being taken off on a stretcher and replaced by recent signing Dean Holden.
Four minutes before the interval, Hearts should have scored.
Hartley's mazy run took him across the edge of the penalty area and his pass set up Mikoliunas in acres of space but the winger's shot struck the crossbar and rebounded to safety.
The match sparked to life midway through the second half as both sides hit the woodwork.
A cross from Hartley rebounded off Velicka's body and struck Schmeichel's right-hand post.
With Falkirk sweeping forward, Liam Craig's superb centre was headed goalwards by the supporting Vitor Lima and with Banks beaten the ball rolled across the goalmouth after hitting the upright.
The Bairns were left to rue that miss as they went behind in the 73rd minute to a goal made by all three substitutes.
Tall won possession in the centre circle and burst forward as the Falkirk defence backed off. The stopper's ball wide found Driver and his low cross was turned in from six yards by Bednar.
Falkirk responded by throwing on strikers Tam McManus and John Stewart for defenders Uras and Jack Ross.
But as the visitors sought a way back into the match they found themselves down to 10 men as Barr saw red.
The youngster had been hacked down by Velicka and reacted furiously by clashing with the Lithuanian, who appeared to make the most of the situation as he fell to the ground.
However, referee Steve Conroy produced the red card amid angry scenes which saw Holden and Velicka also cautioned.
Teams
Hearts Banks, Karipidis, Zaliukas (Tall 61), Berra, Fyssas,Mikoliunas (Driver 67), Hartley, Aguiar, McCann, Velicka,Mole (Bednar 52).
Subs Not Used: Kurskis, Wallace, Pospisil, Brellier.
Booked: Karipidis, Velicka.
Goals: Bednar 74.
Falkirk Schmeichel, Barr, Uras (McManus 80), Dodd (Holden 33),Ross (John Stewart 81), Cregg, Lima, Craig, Scobbie, Gow,Latapy.
Subs Not Used: Lambers, Thomson, Roberston, Mcstay.
Sent Off: Barr (90).
Booked: Holden.
Att: 17,247
Ref: S Conroy (Scotland).