Celtic's hopes of a domestic treble were extinguished as David Raven sent Inverness Caledonian Thistle into their first-ever Scottish Cup final.
The Hoops will feel a sense of injustice after Caley Thistle's Josh Meekings escaped a red card with Celtic leading 1-0 through Virgil van Dijk.
But it was Celtic who lost a man when keeper Craig Gordon was sent off.
Greg Tansey's penalty and Edward Ofere put Caley Thistle ahead, John Guidetti levelled, then Raven secured the win.
That close-range finish three minutes before the end of extra time denied the Scottish Premiership leaders the chance to lift the Scottish Cup for a 37th time and add to the Scottish League Cup they had already secured. Instead, it was third time lucky for Caley Thistle in a Scottish Cup semi-final and it is John Hughes' side who progress to the 30 May final against Championship outfit Falkirk.
Hughes not surprisingly stuck with the same outfield personnel that held Celtic to a 1-1 league draw last weekend but appeared to wrong-foot his opponents by switching to a more ambitious formation with two up front.
With poise and slick passing, the Highland side quickly dispelled any thoughts of a rearguard strategy and had Celtic looking anything but Scottish champions elect in the opening minutes. Celtic manager Ronny Deila was forced into some frantic arm-waving on the touchline and it had the desired effect as Celtic were shaken out of their early jitters.A blistering Nir Biton drive crashed off the outside of the post and a strike from Leigh Griffiths, given a starting role ahead of Guidetti after his midweek hat-trick, was pushed away by goalkeeper Ryan Esson.Now exploiting that additional space in midfield, the extra spring in Celtic's step had Caley Thistle repeatedly exposed on the counter attack.When Gary Warren hauled down James Forrest a couple of yards outside the penalty box, Van Dijk's sublime curling free-kick over the defensive wall gave Esson no chance as it crashed into the back of the net off the inside of the near post.Powerful drives from Stefan Johansen and Kris Commons had Esson, starting in place of the injured Dean Brill, making claims for the man of the match award amid waves of Celtic attacks before the half finished in controversy.When the ball fell to Griffiths at the back post, Meekings' outstretched hand prevented the striker's header finding the net, but referee Steven McLean did not blow his whistle.The Caley Thistle defender should have been sent off and, instead, it was Celtic who were left short of a man 13 minutes into the second half.Marley Watkins beat Adam Matthews to a through ball and was pulled down by Gordon, with Tansey beating substitute goalkeeper Lukasz Zaluska from the resulting penalty.Celtic were bolstered by a sense of injustice, but with left-back Graeme Shinnie and midfielder Ryan Christie in inspirational form, Caley Thistle were in the ascendency as the game entered extra time.The otherwise anonymous Ofere drove low past Zaluska from Watkins' knock-down to give Caley Thistle the lead, but then Esson misjudged substitute Guidetti's free-kick and allowed it to bounce in front then behind his prone frame to give Celtic renewed hope.However, having already missed an open goal to restore the lead, substitute Nick Ross made amends by setting up Shinnie to fire across goal for the waiting Raven to power a winner past Zaluska that will go down in history alongside that moment 15 years ago when the-then First Division outfit knocked Celtic out the same competition.