First-half goals from Stilian Petrov and John Hartson paved the way for Celtic to move to within four points of the league leaders with two games in hand. Craig Bellamy, with his first league goal for the club, cemented the victory.
It was a dominant display by Celtic as they scored early and did not allow Hibs a chance to turn the game as they pressed their opponents all over the pitch.
Hibs were without Antonio Murray due to a hip injury, but Celtic were unchanged from the team that dismantled Dundee in midweek.
Celtic got into their stride early and were in front after four minutes. Chris Sutton provided the cross and when Hartson failed to get on the end of it, Petrov nipped in to beat Simon Brown with a calm finish.
The pace of Bellamy stretched the Hibs' defence and the Welsh striker came close shortly after the goal with a shot which was deflected for a corner.
Hibs were second to every ball at this stage as Celtic took control of the midfield.
Garry O'Connor was wayward with an ambitious 30-yard shot which was well off target.
Hibs had a good spell midway through the first half and Rab Douglas did well to pluck a David Murphy cross off the head of O'Connor.
But there was no cutting edge to the Edinburgh side and their defence was caught out again when Celtic scored their second after 31 minutes.
Sutton produced a great early cross which was touched on by Bellamy and Hartson clipped the ball into the net.
It was Sutton's last involvement as he suffered a pulled hamstring making the cross and he was replaced by Aiden McGeady.
Hibs had a chance to pull a goal back before half-time when Bobo Balde was hopelessly short with a pass back and Derek Riordan pounced.
But Douglas stood up strong and managed to get a touch to the striker's shot before Stanislav Varga made the final clearance.
Hibs replaced Alen Orman with Guillaume Beuzelin at half-time, but Celtic continued to hold the upper hand.
Varga was just inches away from getting his head to a McGeady corner with Simon Brown struggling to cover his goal.
Bellamy had another chance after 63 minutes when a shot from McGeady broke into his path but he shot wildly over the top.
Hibs just could not find a way back as Celtic forced the play and did not ease up with McGeady and Bellamy prominent.
Bellamy added a disputed third after 69 minutes when he galloped onto a through ball from Alan Thompson with the home defence claiming offside and produced an accomplished finish.
The frustration from the stands was obvious when a bottle was thrown on to the pitch and it could lead to Hibs being in trouble with the authorities.
Beuzelin pulled back a late consolation for Hibs deep into injury-time.