Here's how the players fared:
HIBERNIAN
BEN WILLIAMS: Blameless for the first two Falkirk goals, but spilled Lyle Taylor's shot to set up Blair Alston for Falkirk's third. Saved two other decent chances from the striker, though, to keep Hibs in it. 6/10
TIM CLANCY: Shirked a 50-50 challenge with Alston 10 yards from his own box in build-up to Falkirk's third goal and remained nervy even as Hibs gained confidence. 5
PAUL HANLON: Barely won a header in the first half and was given the run-around by Taylor and his colleagues. Still shaky even after the fightback began. 5
JAMES McPAKE: As culpable as his team-mates in the first 45 minutes but led by example thereafter, throwing himself into some must-win tackles. 6
RYAN McGIVERN: On-loan from Manchester City, this was not the kind of display that will convince Roberto Mancini that the Northern Irishman is a future replacement for Gael Clichy. 6
JORGE CLAROS: Failed to check Craig Sibbald's run as Falkirk struck first and looked shell-shocked by the pace and movement of his opponents. Found his feet in second half. 6
ALEX HARRIS: Quiet in the first half as Hibs floundered, but fired up the Hibs comeback when he was switched from right to left flank. Saw a shot pushed onto the bar before getting his team motoring with a deflected 20-yard strike. 8
SCOTT ROBERTSON: Fell to pieces after a horror miss from 10 yards out in the moments following Falkirk's first goal. Substituted after 32 minutes. 3
KEVIN THOMSON: Booked after tugging back Alston inside 20 minutes. Looked sluggish as the Falkirk youngsters buzzed around him. Replaced early in the second half. 5
PAUL CAIRNEY: Caught napping for Falkirk's second as Fulton stole a march to head home. Another one who paid the price for a desperate display when he was subbed at the break. 4
LEIGH GRIFFITHS: Missed seven chances - including a penalty - before finally netting Hibs' second. An erroneous offside call denied him another in extra time but he was not to be denied and lashed home stunning winner with extra time looming. 8
Substitutes:
DANNY HANDLING (for Robertson, 32): Introduced with Hibs all at sea but helped add stability at start of second period as well as winning a penalty. 4
EOIN DOYLE (for Cairney, 46): Made his mark by netting spectacular equaliser with seven minutes left of the 90. 5
TOM TAIWO (for Thomson, 64): Injected some much-needed pace into heart of the Edinburgh side's midfield. 3
FALKIRK
MICHAEL McGOVERN: Could do nothing as Darren Dods' touch took Harris' shot away from his reach but pulled off brilliant save to keep out Griffiths' penalty. 7
KIERAN DUFFIE: Found himself up against a livewire as Harris grabbed the game by the scruff of the neck after the break. 6
DARREN DODS: Had it easy in the first half but the second was a different story. Deflected Harris' strike past McGovern and was lucky to avoid handing Griffiths a penalty just before the end of normal time. 5
JONATHAN FLYNN: Won the header which led to Fulton's goal but struggled after the break as Hibs piled on the pressure. 6
STEPHEN KINGSLEY: Kept Harris quiet in the first 45 minutes and was alert to match the run of Griffiths as he attacked a ball to the back post. 7
STEWART MURDOCH: Booked after tripping Handling inside the box - grateful when Griffiths fluffed the spot-kick. 6
CRAIG SIBBALD: Kept his composure on the edge of the box to slot home the opening goal, while his passing display was flawless. 7
JAY FULTON: Haunted by a costly miss in League Cup semi-final defeat to Celtic last season but made no mistake this time as he darted in to head home Falkirk's second goal. 8
CONOR McGRANDLES: Provided the hook shot which teed up Fulton for the second and his energy in midfield was impressive too. Tired after the interval and was substituted. 7
BLAIR ALSTON: Pounced when Clancy lacked desire for a loose ball to set up Taylor and kept running to ram home the third when the ball bounced free from Williams' grasp. 8
LYLE TAYLOR: Provided perfect cut-back for Sibbald's goal and was involved again for the third. Should have put Falkirk four up soon after and missed late chance to level in extra time. 6
Substitutes:
THOMAS GRANT (for Alston, 64): Replaced Alston and gave a nervy Clancy just as much to worry about with a couple of driving runs. 3
DAVID WEATHERSTON (for Fulton, 73): On for Fulton but could not do much to stem Hibs' attacking tides. 2
SEAN HIGGINS (for McGrandles, 79): Received limited service and made little impact. 2
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