The dominant Easter Road side hit the post just before the break through Fraser Fyvie and again in the second half through fellow midfielder Scott Allan, with the Bairns rarely threatening.
However, the Hibees were stunned in the 74th minute when Falkirk midfielder Craig Sibbald headed in a Blair Alston cross to set up a meeting on May 30 with either Inverness or Celtic.
It was sweet revenge for the Bairns, who lost a seven-goal thriller to the Leith side at the same stage of the competition two years ago, and they will be looking to take the cup back to the town for the first time since 1957.
For their part, Hibs, last winners of the trophy in 1902, will wonder if that curse will ever be broken after a semi-final in which they had bossed for long spells.
Both managers were forced into changes for the all-Championship last-four tie.
Hibs midfielder Scott Robertson replaced Martin Boyle who is cup-tied after playing for parent club Dundee in the competition before his loan move to Easter Road.
Falkirk manager Peter Houston had John Baird and Mark Kerr cup-tied and top scorer Rory Loy failed to recover from an ankle injury as captain David McCracken returned to defence with forward Taylor Morgan given a start.
Falkirk went into the game undefeated in three league games against Hibs this season, drawing two and winning one, but found themselves under pressure from the first whistle.
Indeed, Houston's side were lucky to escape going behind after only six minutes when Dylan McGeouch's fine cross from the right was directed toward his own goal by the foot of the stretching McCracken
F alkirk goalkeeper Jamie MacDonald chested it straight to the falling former Falkirk striker Farid El Alagui but, while flat on the ground, he headed straight into the arms of the grateful Bairns keeper
The Bairns hit back immediately.
Midfielder Will Vaulks' long-range drive was deflected past the post as Hibs withstood a brief spell of pressure, with McCracken heading a Sibbald corner just past the near post.
The tempo then subsided, as if both teams had surprised themselves with their early boldness.
Hibs were the slicker but their final ball was lacking and so was their luck, it appeared.
Two minutes from the break, after El Alagui had hit the side-netting, Fyvie's low drive from around 30 yards beat MacDonald.
However, the ball bounced off the post and back to the keeper who, like the Falkirk fans, again breathed a sigh of relief.
Houston replaced David Smith with Botti Biabi for the start of the second half but, in the 47th minute, it was Alston who forced Hibs keeper Mark Oxley to push his 25-yard shot round the post for a corner, which came to nothing.
The Easter Road men then dominated.
In the 64th minute, as they pinned Falkirk back in their box again, McGeouch got his legs tangled trying to execute a volley before Lewis Stevenson skied his close-range shot high over the bar.
Then Allan brilliantly weaved his way into the Falkirk penalty area before driving against the bar, with El Alagui heading his corner over moments later.
But the Hibees were stunned when Falkirk took the lead.
There was little imminent danger when Alston got past Robertson down the right, but he whipped in a delightful cross and Sibbald escaped the attention of McGeouch to power a header past Oxley.
Reeling Hibs threw everything forward in search of a leveller.
A Paul Hanlon tackle prevented Biabi getting his shot away on the counter - Falkirk cries for a penalty were dismissed by referee John Beaton - before MacDonald made a crucial save from El Alagui at his near post.
Falkirk then held out for the three minutes of added time to spark scenes of joy among players and fans at the final whistle.
Source : PA