Celtic dug out yet another narrow win on their inexorable march towards the defence of the league title.
Craig Beattie was on target for Celtic
Craig Beattie powered a header home after the break, racing on to a fine flighted pass from Aiden McGeady.
It was just reward for the lumbering striker who worked hard all day and caused Hibs numerous problems.
Guillaume Beuzelin twice went close for Hibs in the first half but the visitors ran out of steam when Ivan Sproule was sent off late in the game.
Celtic started with impressive cohesion, with the lively Kenny Miller flashing a close-range header past the near post with only two minutes gone.
Beattie then missed a decent chance from a Shunsuke Nakamura corner, failing to connect properly with his header from eight yards.
Hibs immediately sprang on the counter-attack and should have scored when Michael Stewart sent Beuzelin clear of the chasing Celtic defence.
But, with only keeper Artur Boruc to beat, the French midfielder drove narrowly wide of the target from 20 yards.
The visitors were growing in confidence but it was Celtic who were next to threaten when Beattie's angled shot from 16 yards was saved by Andrew McNeil.
In the 38th minute a first-time pass from McGeady sent Paul Hartley through but defender Shelton Martis got a great block in and the ball rolled kindly through to McNeil.
As the interval approached Beattie headed a Lee Naylor cross over the bar.
Celtic and Hibs failed to sparkle in a scrappy match
But Hibs were not for lying down and Boruc then had to make two good saves to keep out long range efforts from Sean Lynch and Beuzelin.
Celtic started the second half very strongly and the visitors were defending desperately at the edge of their own penalty box.
So it was no surprise when the home side made the breakthrough on 54 minutes when Beattie ran on to a McGeady cross and crashed a header beyond McNeil.
Having gone ahead, Celtic were content to hit on the break and Miller raced through on goal only for Chris Hogg to make a great sliding challenge to deny the Scotland striker.
Hibs substitute Abdessalam Benjelloun flashed a dangerous ball across the face of goal when he perhaps had time to pick out team-mate Steven Fletcher in a good position.
A slip from Stephen McManus almost gifted a chance to Sproule but the Hibs replacement was not quick enough to react and he was robbed by Naylor.
Benjelloun then fed a cute ball to Sproule but the Northern Ireland international dithered again, electing to try and find a pass rather than shooting and Naylor was on hand to clear up.
Sproule was having a bad day and it got worse when he was shown a straight red card for a late tackle on Naylor after 86 minutes.
Celtic: Boruc, Wilson, Pressley, McManus, Naylor, Nakamura, Lennon, Hartley, McGeady, Beattie, Miller (Gravesen 78). Subs Not Used: Brown, O'Dea, Sno, Jarosik, Telfer, Sheridan.
Booked: Hartley. Goals: Beattie 54.
Hibernian: McNeil, McCann, Martis, Hogg, Murphy, Stewart (Sproule 46), Beuzelin, Scott Brown, Stevenson, Fletcher, Lynch (Benjelloun 59). Subs Not Used: Simon Brown, Shiels, Morrow, McCluskey, Chisholm.
Sent Off: Sproule (86). Booked: Stevenson.
Ref: S Dougal