Both sides struggled to find their rhythm in the opening stages of the game as a swirling wind and driving rain made for terrible conditions at the Falkirk Stadium.
There was an early booking for the Bairns when midfielder Gary Miller picked up a yellow card after a fairly innocuous challenge on Marcel Langer.
Neither side was able to make anything happen going forward as the game got bogged down in midfield as the conditions progressively worsened.
With a dearth of any real action on display, referee John Beaton was the centre of attention with a series of baffling calls as he infuriated both sets of fans.
As half-time neared, Falkirk started to find some gaps in the Hearts defence as the League One side looked to take the lead but struggled to test Man United loanee, Joel Pereira.
The Jambos keeper almost gift-wrapped the opener for Falkirk, struggling to deal with a cross from the left flank before gathering it at the second attempt.
Falkirk really should have been 1-0 up when Josh Todd reacted quickest to a ball over the top from Robbie Mutch but screwed his shot wide of the target with the Hearts defence all over the place.
Hearts finally got a shot on goal, after some good work by Steven Naismith found Liam Boyce in a bit of space but the January signing could only fire his shot right down Mutch’s throat in the last real action of the opening period.
It was the Bairns who took the early initiative before John Beaton again himself centre of attention with the staggering decision to award Hearts a penalty just minutes after the restart.
Sean Clare cooly netted from 12 yards but, on first viewing, it is one the referee won’t want to see again after appearing to get it badly wrong.
Going one down didn’t seem to deter the Bairns as they immediately went up the pitch and came within inches of grabbing an equlaiser in a goalmouth scramble.
The Bairns kept pressing and, in an opening ten minutes of the second 45 that was more entertaining than the entire first-half, Declan McManus rattled the base of Pereira’s post.
The goal also sparked the quiet 2000 Hearts into life and the North Stand started making noise for the frst time of the evening.
There was little in the action of the pitch which would have made it clear which side was the Premiership team and which was the League One side as the Bairns again came close to drawing level through Gary Millar’s free-kick – with only the crossbar denying the Falkirk midfielder.
The Jambos made the first change of the night with skipper Stevie Naismith going off to a chorus of boos from the home support to be replaced by Jamie Walker.
Hearts then started taking a bit more control of the game and making the ball do wthe work for them as they made Falkirk chase it for long spells – however the game started to become quite scrappy with individual errors saw both sides gift the other possession.
With the game threatening to run away from Falkirk, Bairns made three changes in quick successios as Louis Longridge, Charlie Telfer and David McMillan replaced Mo Gomis, Connor Sammon and Aidan Connolly for the final 20 minutes.
It was a very attack-minded set of changes from Lee Miller and David McCracken and showed that the Falkirk bosses still hadn’t given up on a place in the last eight of the competition.
The changes put Falkirk back on the front foot and the Bairns were again on top as the clock ticked down on their Scottish Cup ambitions.
It really should have been 2-0 for Hearts after the ball broke to an unmarked Euan Henderson in the area but the Jambos ace somehow contrived to fire over.
Despite their best efforts, the Bairns couldn’t find a way through but can be more than happy with how difficult they made life for a team two leagues above them as their unbeaten run under Miller and McCracken finally came to an end.