Henrik Larsson hit two goals to become Celtic's all-time third top scorer as Hibs were swept aside at Easter Road.
Henrik Larsson claimed two goals at Easter Road
The striker took his Celtic tally to 233 goals thanks to a couple of simple finishes either side of the interval.
Didier Agathe put the visitors in front after 18 minutes when he slid in to poke home a Stephen McManus cross.
Agathe helped himself to another goal ten minutes from time when his shot from a tight angle squeezed through keeper Daniel Andersson's legs.
The visitors had an early chance when a long ball caught the Hibs defence napping and Larsson was able to pick out Stilian Petrov but the Bulgarian shot straight at Andersson.
Hibs replied almost immediately when full-back Steven Whittaker hit a difficult volley that had David Marshall scrambling to push the ball round the post.
The home team were moving the ball around well and Scott Brown was causing Celtic problems with his pace and close control.
But it was Celtic who went in front when a speculative cross from McManus flashed across the penalty box and Agathe beat the dithering Roland Edge to steer the ball in via the post.
Agathe should have doubled his tally a minute later when Andersson pushed an angled shot from Pearson into his path but the winger mis-timed his lunge and the ball bounced over him just a few yards from goal.
Pearson then put Petrov clean through on goal but the midfielder tried to pick out Agathe at the back post instead of going for goal and the chance was wasted.
Stephen Dobbie came close for Hibs when he fired a 20 yard free-kick narrowly past the upright.
Petrov again wasted a glorious chance in the 31st minute when he broke free in the box but again shot straight at Andersson.
Henrik Larsson watches his second goal roll in
Celtic did extend their lead after 35 minutes and it was more calamitous defending that led to Larsson claiming his first of the day.
Andersson opted to let a long ball bounce into his area but his more celebrated Swedish compatriot nipped in to steal the ball from his fingertips on the edge of the box and rolled the ball into an empty net.
Shortly before the break Neil Lennon was fortunate not to concede a penalty when he had a sly kick at Brown as Hibs were taking a throw-in.
Celtic began the second half in determined mood and were further ahead after 49 minutes when Larsson ran on to a Lennon pass and slotted the ball through Andersson's legs.
With the points wrapped up and Barcelona to face on Thursday, Celtic manager Martin O'Neill made changes - taking off Larsson, Lennon and Paul Lambert.
Dobbie had a powerful strike comfortably saved by Marshall and Whittaker was denied a consolation goal when Pearson cleared from the goal-line.
In the 80th minute Hibs' miserable afternoon was compounded when the ball broke to Agathe and his low shot found its way through the legs of the luckless Andersson.
Worse was to follow for the home team when teenage defender Jonathan Baillie was red carded in the dying stages for clashing with Celtic substitute Craig Beattie.
Hibernian: Andersson, Smith, Whittaker, Edge, Baillie, Caldwell, Nicol, Reid (Riordan 68), Scott Brown, Dobbie (Zambernardi 73), McManus. Subs Not Used: Alistair Brown, McCluskey, Orman.
Celtic: Marshall, McNamara, Balde, Kennedy, McManus, Agathe, Lennon (Mjallby 63), Lambert (Smith 68), Pearson, Larsson (Beattie 63), Petrov. Subs Not Used: Douglas, Sylla.
Referee: D McDonald