A howler by Artur Boruc and a Colin Nish goal deservedly gave the home side the points.
It was a cagey start to the match as both sides took their time to settle into the game. Steven Thicot for Hibs and Celtic's Shaun Maloney both passed up half-chances in the early stages, but there was little in the way of goalmouth action.
As the half wore on, Hibs looked very nervy in possession and kept giving the ball away in their defensive third, and only a last-ditch challenge by Ian Murray prevented Cillian Sheridan capitalising on one such error.
Just before the half-hour mark, the side from the capital created the first clear-cut chance of the match. John Rankin played an expertly weighted throughball to Steven Fletcher but, although he rounded the onrushing Boruc, he lacked composure as he fired wide.
At the other end Maloney did well to create himself an opening but, just as he opened up his body to shoot, Rob Jones flew in with a terrific challenge and the ball went wide.
The deadlock was broken ten minutes into the second half when Boruc continued his run of mistakes at Easter Road. After a couple of glaring errors at the same ground last season he was again at fault for Hibs' opener.
Rankin picked the ball up just inside the Celtic half and, seeing nothing on ahead of him, sent a speculative effort at goal from 35 yards. The ball headed straight at the big Pole but it inexplicably slipped by him and into the net.
Celtic went close a couple of times on the hour mark, with Scott McDonald heading over the bar and Andreas Hinkel dragging a shot wide after cutting inside.
After Maloney had again gone close for Celtic, Hibs made it 2-0 in the 69th minute. Speed merchant Alan O'Brien was sent clear and, although Boruc forced him wide, he was able to cross for Rankin to set up Nish for a simple tap-in.
Celtic forced a flurry of corner late on, but were reduced to long-range efforts, none of which troubled Yves Ma-Kalambay in the Hibs goal.