The home team hit Hibs with two early goals from Scott McDonald and skipper Stephen McManus but the visitors were thrown a lifeline when Rod Jones reduced the deficit.
With such a slender lead Celtic looked nervous every time Hibs broke clear, but McDonald calmed their nerves with a clinical finish 14 minutes from time.
It was a thrilling start by the home side. Shunsuke Nakamura's corner was headed powerfully towards goal. Hibs keeper Grzegorz Szamotulski parried the effort only for McDonald to react quickest to force the ball home from close range.
From another Nakamura corner Celtic increased their lead with McManus shooting home after efforts from McDonald and Scott Brown were blocked.
Aiden McGeady was giving Darren McCormack a difficult afternoon and the Celtic winger tested the Hibs keeper twice with powerful shots.
Against the run of play Hibs pulled one goal back when Derek Riordan's free-kick was met by Jones who guided his header past the stranded Artur Boruc. Yet again the Celtic central defence looked exposed.
A mistake by Steven Thicot let Jan Vennegoor of Hesselink clear on goal but the Dutch striker volleyed his effort wide.
Just before half-time the Hibs keeper produced two marvellous saves to deny free-kicks from Nakamura.
The second half started slowly before Hibs threatened on the break. Chris Hogg's long pass found Riordan who crossed first time but Colin Nish delayed too long at the back post and the chance was lost.
Celtic claimed a penalty when McGeady was brought down by McCormack in the box but their appeals were waved away.
The home team secured victory when Brown's challenge held off Lewis Stevenson and, from his clever cut-back, McDonald shot high into the net.
Hibs nearly pulled a goal back when their Hungarian substitute Denes Rosa struck a magnificent 30-yard shot which smacked against the post with Boruc beaten.