After going in at the half-time break three goals behind, strikes from Alex Harris, Eoin Doyle and a double from Leigh Griffiths puts the SPL side into the Scottish Cup final
The First Division side looked to be heading to the showpiece final after strikes from Craig Sibbald, Jay Fulton and Blair Alston had them comfortably ahead, before Alex Harris, Eoin Doyle and a Leigh Griffiths double sent the Easter Road side through.
Hibernian made only the one change from the side that failed to trouble champions elect Celtic at Parkhead last Saturday, with Gary Deegan making way for Paul Cairney.
New Falkirk boss Gary Holt made five changes from the side that thumped Cowdenbeath 4-0, with Liam Rowan, Liam Dick, Thomas Grant, Dale Fulton and Sean Higgins all making way for Kieran Duffie, Stephen Kingsley, Stewart Murdoch, Blair Alston and top scorer Lyle Taylor.
The SPL outfit found themselves a goal down within the first six minutes, as Taylor cut the ball back from the left hand side of the penalty area for Sibbald to smash home for the opener.
Things got even worse for Pat Fenlon’s side after they failed to deal with a long free kick into the box, which allowed Conor McGrandles to find Fulton with a diving header past the helpless Ben Williams.
On the half-hour mark it became embarrassing for the Easter Road side as Taylor broke the offside trap and, after his effort was parried by Williams, Alston had an empty net at his mercy to claim the third and lead to streams of Hibernian fans making their way out of Hampden.
The second half almost started with further misery being piled on Hibernian, as Taylor got onto the end of a long pass, before jinking past a defender and rifling a shot just over Williams bar.
Hibernian, once again through Harris, could have had a goal back with five minutes gone as he had another volley saved by McGovern and Griffiths' rebound was tipped over.
Only a minute later, however, the Easter Road side did get a goal back, and it was third time lucky for Harris, as he cut inside before unleashing an unstoppable 25-yard drive beyond McGovern to give his side hope.
With 20 minutes left Hibernian were handed a golden chance to reduce Falkirk’s lead even further, when Danny Handling went down inside the box under a challenge from Stewart Murdoch, but Griffiths could only look on as McGovern saved his penalty and the resulting rebound.
They did finally reduce Falkirk’s advantage on 77 minutes, when Harris cut the ball back to Griffiths, who made no mistake from six-yards out.
The fightback was complete with eight minutes left as Doyle picked up possession in the middle of the Falkirk half, before letting fly from the edge of the area to equalise.
Griffiths did have the ball in the net just before the end of the first period of extra time, but the assistant referee ruled the on-loan Wolves striker was offside.
With five minutes remaining and the game looking like it was going to penalties, Griffiths stepped up from almost 30-yards and unleashed a stinging drive that nestled in the back of the net to seal Hibernian’s final place.