Henrik Larsson enhanced his legendary status at Parkhead with a classy double as his side destroyed Bobby Williamson's hot-headed youngsters at Easter Road.
Didier Agathe also bagged a brace as the champions-elect regained their 19-point lead over Rangers at the top of the Bank of Scotland Premier League but Hibernian's misery was compounded with the late sending off of Jonathan Baillie
for a head-butt.
The prolific Swedish striker became the club's all-time third top scorer after going beyond Stevie Chalmers' record of 231 goals which he equalled in midweek.
Larsson, who will quit the club in the summer, also surpassed Bobby Lennox's post-war league haul of 167 goals, which he also hit in the victory at Dundee.
His record feat came just days before his side face the hostile and intimidating prospect of the Nou Camp against Barcelona, who he is tipped to join in the summer.
Celtic warmed up for the UEFA Cup showdown in perfect fashion but manager Martin O'Neill was forced to hand 21-year-old Stephen McManus his debut with Stanislav Varga missing while John Kennedy and Paul Lambert also came in for
Alan Thompson and Momo Sylla.
And debutant McManus was involved in Celtic's first threatening thrust forward which almost brought the opener after just two minutes.
His long ball was controlled by Larsson and he found the overlapping Stilian Petrov, who cut inside and fired a right-foot shot straight at Daniel Andersson.
Celtic were again with teenager David Marshall in goal and he needed to turn Whittaker's drive around the post from 22 yards in the fourth minute.
The home side were looking for an optimistic penalty in the ninth minute when Stephen Dobbie went down under the fair challenge of Kennedy.
Hibernian's youngsters looked confident going forward and Celtic needed a vital interception from Lambert to save them in the 15th minute.
Dobbie and Scott Brown combined to give Thomas McManus a sight of goal but the veteran skipper's last-ditch challenge diverted his effort wide.
But Celtic snatched the lead in the 18th minute when Stephen Pearson found Didier Agathe at the back post and although Andersson got a hand to his right-foot shot he could not stop the ball.
The visitors came agonisingly close to extending their advantage in the 19th minute when they exploited the huge gaps in the Hibernian defence again.
Pearson got a slight touch on Neil Lennon's cross and that took it just out of the reach of Agathe's outstretched leg.
They should have been out of sight in the 26th minute when Pearson put Petrov clean through on goal after another good move by the visitors but he tried to
pick out Agathe at the back post instead of going for goal and the chance was
wasted.
Dobbie almost made them pay in the 29th minute when he fired a free-kick, from
the edge of the area, past the upright.
Petrov again wasted a glorious chance in the 31st minute when he broke free in
the box, after good work by Pearson and Lennon, but he blasted the ball straight
at Andersson.
It seemed that Celtic would have to be gifted a second goal and so it proved
in the 34th minute after a shocking mistake by the Hibernian goalkeeper.
He came to catch a Lambert ball, instead of booting it into the stand, and
Larsson nipped in to snatch the ball away from him before slotting the ball into
an empty goal.
It took Celtic just three minutes of the second half to put the game beyond
Hibernian's reach following a superb passing move which was finished off
inevitably by Larsson.
Pearson played the ball in field to Lennon and he threaded the ball through to
Larsson in the box and he nonchalantly steered the ball through the legs of
Andersson.
O'Neill could afford the luxury of taking off Larsson and Lennon with
Barcelona in mind and bringing on Johan Mjallby and Craig Beattie.
The Swedish defender's long-awaited return from injury was also timely with
Balde suspended for Thursday and Varga and Chris Sutton doubtful.
Both managers made changes in the 67th minute with Jamie Smith coming on for
Lambert and Alan Reid being replaced by Derek Riordan.
Stephen McManus was enjoying a good debut but he earned himself a yellow card
in the 71st minute after clipping the heels of Brown.
Dobbie was stretchered off moments later to give Hibernian manager Bobby
Williamson more concern after making five changes to his side.
The home side almost snatched a consolation in the 75th minute but Pearson was
on the line to prevent Whittaker's shot going over the line.
But Agathe added insult to injury in the 80th minute when Agathe took
advantage of more shoddy defending by Hibernian to force the ball past
Andersson.
After losing the CIS Insurance Cup final to Livingston last week, Hibernian
again lost their heads and McManus was booked after attempting to kick Agathe up
in the air.
It was no surprise then that Baillie was given a straight red card before the
end for head-butting Beattie in the chest after the Celtic player had fallen on
him.
Teams
Hibernian Andersson, Smith, Whittaker, Edge, Baillie,
Caldwell, Nicol, Reid (Riordan 68), Scott Brown,
Dobbie (Zambernardi 73), McManus.
Subs Not Used: Alistair Brown, McCluskey, Orman.
Sent Off: Baillie (88).
Booked: Nicol, Andersson, Caldwell, McManus.
Celtic Marshall, McNamara, Balde, Kennedy, McManus, Agathe,
Lennon (Mjallby 63), Lambert (Smith 68), Pearson,
Larsson (Beattie 63), Petrov.
Subs Not Used: Douglas, Sylla.
Booked: McManus, Kennedy.
Goals: Agathe 18, Larsson 35, 49, Agathe 81.
Att: 9,456
Ref: D McDonald (Scotland).