Late goals from Simon Murray and Paul Dixon sent Dundee United into the Scottish Premiership play-off final.
James Craigen had given Falkirk the lead in the semi-final second leg, after the first meeting ended 2-2.
But in the final 15 minutes, Murray, then Dixon, found the net to send the visiting supporters into raptures.
United's dramatic victory sets up a two-legged final against Inverness Caledonian Thistle or Hamilton Academical for a top-flight berth.
The Premiership's bottom two battle to avoid finishing last, and suffering automatic relegation, on Saturday.
Dixon's 87th-minute winner, his first goal in more than five years, puts United into the first leg of the play-off final, at Tannadice on Thursday, before the top-flight side host Ray McKinnon's men on Sunday, 28 May.
The away support stayed long after the final whistle to chant and sing about their team, especially happy given that they had trailed for a large part of the match.
Craigen has scored five goals this season and three of those have been against United.
His scissor-kick finish in the first leg was spectacular and his excellent technique came to the fore again this time as he kept the angled drive low at the edge of the box, following good work by John Baird and Aaron Muirhead.
The Falkirk Stadium had not been a happy hunting ground for the Tangerines, with 3-0 and 3-1 defeats already experienced this season.
Friday's match was the visitors' fifth game in 14 days, having already overcome Morton in the play-off quarter-finals, and McKinnon commented before the match that dips in the North Sea at St Andrews had been part of their team-building.
For parts of the first half some players were indeed all at sea and seemed a bit nervous - Mark Durnan on one occasion almost having a serious mix-up with goalkeeper Cammy Bell.
But towards the end of the opening 45 minutes United settled and created a few chances.
Thomas Mikkelsen headed and curled two separate efforts over, while Murray fluffed his lines after a nice Tony Andreu cut-back.
That theme continued after the break as the visitors were encouraged by shooting towards the away support.
Those fans were celebrating when William Edjenguele's eight-yard volley crashed in off the crossbar but referee Kevin Clancy whistled for a foul when he saw Mikkelsen leaning into Paul Watson.
Undeterred, Murray set up Andreu who turned his effort round the wrong side of the post, before Bairns goalkeeper Robbie Thomson held Murray's header tightly.
Despite their calmness, Falkirk had gone a while without troubling Bell until Craigen's left-footer spun wide of the post.
From that moment on the night was United's.
Blair Spittal flicked on a long ball and Muirhead got the ball caught under his foot, which allowed the potent Murray to steal in and side-foot beyond Thomson.
Substitute Alex Nicholls was only on the pitch because of an injury to previous substitute Scott Fraser.
But the Englishman floated in a great cross for Dixon, who might have pushed Tom Taiwo slightly as he raced in to send a looping header over Thomson.