Falkirk 3 Hibs 2 (Falkirk won 5-4 on aggregate)
Late goal specialist Bob McHugh struck again as Falkirk came from behind to dash Hib's promotion hopes and set up a Premiership play-off final against Kilmarnock.
McHugh pounced in injury time in a crowded penalty box to convert a long throw and secure a 3-2 victory in front of a sell-out 7,851 crowd at the Falkirk Stadium.
The former Motherwell striker helped Falkirk to second place in the Championship with an injury-time winner over Rangers and last-minute leveller at Easter Road, and had struck again in the first leg with an 80th-minute equaliser.
Hibs had looked in control after James Keatings turned the game on its head with two goals in three minutes after a poor first half-hour for the visitors, who trailed to Blair Alston's goal.
But Luke Leahy struck a magnificent equaliser in the 79th minute before McHugh netted with virtually the last kick of the ball.
Falkirk will now host Kilmarnock in the first leg of the final on Thursday while Hibs will have to lift themselves for next Saturday's William Hill Scottish Cup final against Rangers - where they could be missing Dylan McGeouch, who went off injured.
Falkirk started brightly and posed problems with some sharp passing down their left side.
Full-back Leahy was instigating a number of attacks and he was involved in the 13th-minute opener. His ball inside was followed by one-touch passes by Will Vaulks and McHugh which put Alston through, and the midfielder finished past Conrad Logan.
Falkirk remained in control, content to let Hibs pass the ball in front of them before breaking with purpose.
But Liam Henderson's pass changed everything. Keatings got away in the left channel and David McCracken brought him down with a sliding challenge.
The Falkirk defender had got away with a clear handball in the box when Hibs led on Tuesday but Craig Thomson had no hesitation in giving the spot-kick.
Keatings, a surprise inclusion in place of Jason Cummings, converted and soon headed home an Anthony Stokes cross from 12 yards to make it 2-1, and put his team 4-3 up on aggregate.
The striker had another opening when McGinn's cross found him in between the two central defenders but he could not direct his header towards goal.
McCracken headed wide from Alston's corner after the break and Hibs went looking for a third. Henderson and McGinn came close from the edge of the box and Leahy needed to be precise with his goalmouth clearance from David Gray's header.
Hibs looked comfortable but Leahy produced a moment of real class in the 79th minute when he met a headed clearance on the half-volley and guided a powerful shot inside Logan's post from 25 yards.
Paul Hanlon got away with a risky penalty-box barge on Falkirk substitute Lee Miller and the hosts had two late escapes when Cummings fired a 35-yard strike off the bar before Stokes headed inches over from a corner.
Extra time loomed, but McHugh stole the show.