Headed goals by Stephen McManus and Scott McDonald separated the sides. As Hibs tired towards the end they also had two players sent off, Martin Canning for a second yellow and Ian Murray received a red card for a bad foul on Aiden McGeady.
Celtic's sixth win in a row ended Hibs' hopes of a UEFA Cup place and kept the pressure on Rangers, who have two games in hand.
Hibs attacked from the start and after Steven Fletcher's headed drifted wide, Dean Shiels powered in a powerful shot which Artur Boruc did well to parry.
Play swept from end to end and Jan Vennegoor of Hesselink headed past the post from ten yards and, after Andrew McNeil pushed out McGeady's shot, Barry Robson hit the rebound over.
Robson should have done better than head Shunsuke Nakamura's corner wide, before Fletcher tested Boruc again with a well-struck shot which took a deflection off Gary Caldwell.
Celtic's pressure paid off when Nakamura's corner was headed home by McManus.
Nakamura went close to adding to Celtic's lead, but his free-kick came back off the post.
The frantic pace continued in the second half, a clever pass from Nakamura put McDonald through, but after rounding the keeper his shot, was cleared off the line by Murray.
With such a slender lead Celtic were always aware that one slip would undo all their good work. Boruc again produced vital saves to deny Guillaume Beuzelin and substitute Clayton Donaldson before Canning was sent off.
McDonald sealed Celtic's victory when he was on his own at the back post to head Robson's corner low into the net.
There was still time for Murray to be red-carded for a foul on McGeady as the Bhoys kept up their relentless pursuit of the league title.