Danny Galbraith’s stoppage-time winner ensured Hibs returned to the Capital with all three points in a dramatic match at Parkhead.
Hibs’ last victory in Glasgow’s east end was a major blow to the Hoops’ title hopes, with this loss leaving them ten points adrift of league leaders Rangers.
Home boss Tony Mowbray made one change to the side which had beaten St Johnstone 4-1 at the weekend, with left-back Paul Caddis coming in for stopper Glenn Loovens who sustained a face injury in Perth, with Darren O’Dea moving into the centre of defence to partner 18-year-old Josh Thompson.
With only one regular defender in Celtic’s back four, right-back Andreas Hinkel, there appeared the opportunity for the Leith side to take advantage.
But, before Hibs had a chance to test that theory they found themselves behind.
Marc-Antoine Fortune headed the home side into the lead after five minutes from Paul Caddis’ corner-kick, the striker reacting first at the front post to head past Hibs keeper Graeme Smith.
The visitors went to pieces for the next few minutes as Celtic threatened to increase their lead, Fortune going close with another couple of headed efforts.
The game, though, was to take a sudden and surprising U-turn. In the 26th minute, after Artur Boruc had pulled off a fine save to prevent Thompson scoring an own goal with a header, Hibs drew level from the resultant corner.
Derek Riordan crossed from the left and Anthony Stokes nipped in ahead of Boruc to flick his header into the net.
With Celtic rattled and the home fans growling in frustration at how the game had turned, the former Sunderland striker drove just wide from distance.
The first half ended with Celtic striker Georgios Samaras picking up a booking for a late challenge on Smith – a decision which prompted the Hoops fans to jeer referee Iain Brines as the teams trooped off.
Within a minute of the second half starting, Aiden McGeady ran onto a Fortune pass but screwed his shot just wide of the target.
Then, as the home side increased the pressure, Samaras missed his kick altogether in front of goal from Niall McGinn’s volley back into the danger area before Smith made a good save from McGeady’s curling effort from the edge of the box.
Korean midfielder Ki Sung-Yueng replaced McGinn on the hour mark, seconds after the Northern Ireland internationalist had a close-range volley brilliantly blocked by Smith.
Five minutes later Lewis Stevenson and Galbraith came on for Riordan and Colin Nish as the visitors tried to get a foothold in the game again.
But it was Samaras who missed a sitter when he headed Caddis’ cross high over the bar from just six yards out, the Greece internationalist rewarded for his mistake by being immediately replaced by Morten Rasmussen who was making his debut.
In the 82nd minute, as Hibs broke, midfielder Liam Miller appeared to be pushed to the ground by O’Dea inside the Celtic box but referee Brines ignored penalty claims.
As tension grew inside Celtic Park, Chris Hogg sliced his shot wide of the target from Galbraith’s corner.
But in a sensational finale, with seconds remaining, Hibs broke and Galbraith slotted past Boruc for the winner.
Hibs: Smith, Wotherspoon, Hogg, Hanlon, Murray, McBride, Rankin, Miller, Nish, Riordan, Stokes.