A superb late strike from Kevin Thomson sealed a deserved victory for Hibs and booked a CIS Cup semi-final date with Rangers.
Celtic took the lead when Stanislav Varga headed Liam Miller’s corner into the net after 56 minutes.
But Grant Brebner equalised in 64 minutes from the spot after John Kennedy had handled in the penalty area.
Thomson’s strike from 20 yards with eight minutes remaining consigned Celtic to their first domestic loss of the season.
Hibs started well in the blustery conditions and Brebner shot narrowly over the bar from the edge of the box after just four minutes.
It did not take Celtic long to get into their stride, however, and Henrik Larsson ought to have done better with a header wide from Alan Thompson’s free-kick after 14 minutes.
Hibs came within inches of taking the lead in rather fortuitous fashion midway through the first half.
Derek Riordan curled in a wicked cross from the left, which deceived Rab Douglas and came back off the frame of the goal only for Scott Brown’s follow-up to be blocked. Chris Sutton came equally close shortly afterwards when Thompson’s shot ricocheted kindly into his path, but his controlled volley came back off the bar with the keeper beaten.
Tam McManus forced Douglas to look lively with a shot on the turn in the closing minutes of the first half, but Garry O’Connor passed up the best chance of the game shortly after the interval.
The striker found himself through on goal with only the keeper to beat, but his shot was too straight and Douglas pulled off a fine save.
Hibs were made to pay for that when Varga rose to head Miller’s corner past Andersson, despite Kevin Thomson’s valiant efforts to prevent the ball crossing the line.
But the home side were handed a lifeline eight minutes later when Kennedy misjudged a cross, allowing it to hit his arm and referee John Rowbotham had no hesitation in awarding a penalty.
Brebner gave Douglas no chance with an excellent spot-kick.
Kennedy almost made amends with 18 minutes remaining when he met a Thompson free kick only to see his effort fly just over.
Larsson went close with a scuffed shot from six yards that Andersson gathered but it was Hibs who took the lead with eight minutes left.
Celtic were unable to clear as Hibs pressed and when the ball fell to Thomson 20 yards out, he fired a sweet left-foot shot past Douglas.
The woodwork denied Hibs again in the final minute – Scott Brown hitting the post – and then Larsson spurned the chance of a late equaliser when he headed over the bar from close range.
Hibs: Andersson, Baillie, Smith, Doumbe, Whittaker, McManus (Dobbie 77), Brown, Brebner, Thomson, Riordan, O’Connor.Subs Not Used: Hyldgaard, Nicol, Reid, Shields
Celtic: Douglas, Varga, Balde, Kennedy, Crainey, Miller, Lambert (Beattie 81), Thompson, Wallace, Larsson, Sutton (Maloney 50). Subs Not Used: Laursen, Guppy, Marshall
Referee: J Rowbotham (Scotland)