Championship strugglers Morton took a famous scalp as Dougie Imrie's penalty knocked Celtic out of the League Cup.
Despite building early pressure, Celtic failed to show composure in front of goal in a scoreless first 90 minutes.
And the Greenock outfit made them pay, Imrie scoring from the spot in extra time after defender Efe Ambrose was penalised for handball.
Celtic, second in the top flight, pressed for a leveller but Morton held on for a memorable win.
The Scottish League Cup remains the one domestic trophy
Celtic boss Neil Lennon
has yet to win and he will need to wait at least another season after Allan Moore's side booked their place in the quarter-finals.
Morton defended superbly at Celtic Park to claim a memorable Cup scalp
Visiting goalkeeper Nicolas Caraux was in inspired form to thwart Celtic time and again as the champions proved profligate.
Charlie Mulgrew tested Caraux with a free-kick as the hosts sought to turn their early territorial advantage into a goal.
The visitors, who sit second bottom of their division, were content to give Celtic possession and attempt to hit them on the break.
Celtic, struggling to breach a spirited Morton rearguard, threatened through Tom Rogic 10 minutes into the second half but Caraux was ultimately untroubled.
The visitors then appealed for a penalty when Fouad "Fred" Bachirou took a tumble on the edge of the area, but the referee waved them away.
With Celtic unable to profit from a succession of corner kicks, the tie went into extra time and Morton took the lead from the spot in the 97th minute.
Ambrose was penalised for handball and Imrie, proving to be the coolest man inside Celtic Park, fired home to send the Morton fans wild.
Virgil van Dijk won countless headers inside the box as Celtic pressed for an equaliser but chances for Mikael Lustig and Mulgrew were spurned as Morton held on for their first win at Celtic Park since 1971 and their first over Celtic since 1985.
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