Captain Scott Brown, who returned after injury, gave the Hoops a fifth-minute lead with a powerful volley which Glenn Loovens added to just after the break when he headed in a Shaun Maloney corner.
Before that, the visitors, now with one win in nine this season, had failed to lay a glove on the Parkhead side.
Former Celtic striker Derek Riordan pulled a goal back with a delightful chip to set up a nervy end to the game but Neil Lennon's men held on to their lead to leapfrog their Old Firm rivals who play at Aberdeen on Sunday.
There was some debate over whether Brown deserved to come back into a team that had demolished Inverness 6-0 in midweek but the former Hibernian midfielder repaid Lennon's enormous faith in him by grabbing the opener.
The game was settling down when Brown broke forward from midfield and worked a one-two with Anthony Stokes, a recent signing from Easter Road, before volleying past goalkeeper Mark Brown from 16 yards, his first goal since March.
Celtic took full control of the game albeit without testing Brown again for a while as the visitors struggled to muster the confidence to emerge from their own half.
But there was always a Celtic threat and in the 24th minute Hibs defender Francis Dickoh was booked by referee Calum Murray for tripping Joe Ledley as the midfielder tried to race clear down the left.
Six minutes later, there was a little more controversy when Stokes was booked for going down too easily in the Hibs box after going past midfielder Liam Miller.
Celtic striker Gary Hooper and busy midfielder Efrain Juarez had efforts just before the interval but failed to test Brown.
Defender Charlie Mulgrew was replaced by midfielder Ki Sung-Yueng at the interval with Ledley moving to left-back and the game resumed its first-half pattern of Celtic dominance.
Three minutes into the second half Stokes had a toe-poke from the edge of the box saved by Brown at the second attempt.
Two minutes later an inexplicable slack pass back from the former Hibs player in the right-back position gave Riordan a good chance which he spurned.
In the 51st minute the points appeared to be safe when Loovens headed in Maloney's corner from the right, the ball adjudged to have gone over the line despite the best efforts of John Rankin to clear.
However, the visitors gave themselves an unexpected lifeline three minutes later when Riordan, with the most delicate of chipped shots from the edge of the box, beat Celtic's giant goalkeeper Fraser Forster.
As the mood inside Celtic Park changed, Hibs sensed there might be a way back and began to move forward with some purpose.
Georgios Samaras, who had been dropped despite scoring a hat-trick against Inverness in midweek, replaced Hooper in the 70th minute and Celtic began to reassert themselves.
In the 81st minute, after Stokes' pass across the six-yard box had just evaded Samaras, Juarez headed Cha Du-Ri's pin-point cross against the crossbar from eight yards when he should have scored.
There were plenty of nervous moments in the closing stages as the home side struggled to kill the game off but the win, when it was confirmed by the full-time whistle, was deserved.