Kilmarnock 0-5 Celtic
Chris Sutton slots in his first goal of the day
Kilmarnock were out-played and out-fought by Celtic who made it 10 straight wins in the league.
Celtic were on top throughout, but had to wait until the later stages to confirm their victory as Kilmarnock defended in numbers.
Chris Sutton opened the scoring with a 20th minute penalty, but it was a full 50 minutes later before John Hartson doubled the lead.
Sutton made it 3-0 before substitute Shaun Maloney got in on the act and then Sutton completed his hat-trick with a late penalty.
Celtic dominated possession in the opening stages without troubling Francois Dubourdeau in the Kilmarnock goal, but they went ahead with their first effort on target.
That came from the penalty spot after Stilian Petrov, looking to get on the end of a one-two with Henrik Larsson, went down under minimal contact from Gary McDonald in the box.
Sutton confidently despatched the spot-kick past Dubourdeau.
A few minutes later it took a wonderful goal-line clearance from Gordon Greer to prevent Celtic going two ahead after Liam Miller latched onto Larsson's pass to lob the ball over Dubourdeau's head.
Kilmarnock put together their first decent move of the game after 37 minutes and it almost led to the equaliser.
Paul di Giacomo's flick found Greg Shields, who got the break of the ball before firing a shot through the legs of Stan Varga but narrowly wide of the post.
There was a major let-off for Kilmarnock just before half time when Sutton slipped the ball to Larsson who turned his marker in the box before clipping the ball past Dubourdeau, only to see it come back off the inside of the post.
Celtic continued to dominate possession at the beginning of the second half, but Magnus Hedman was brought into the game for the first time in 64 minutes when he dived to his left to keep out McDonald's stab at goal.
Moments later, Killie claimed for a penalty when Jackie McNamara seemed to hold back Colin Nish, but referee Hugh Dallas saw nothing amiss.
John Hartson celebrates his goal
Miller flashed a shot a yard wide following Hartson's lay-off as the game at last threatened to come to life.
On 70 minutes Celtic made sure of the points when Michael Gray swung the ball in from the left, Sutton flicked on at the near post and Hartson headed emphatically past Dubourdeau.
Six minutes later it was 3-0 as Hartson played the ball wide for Larsson who whipped it back into the six-yard box for Sutton to bundle it into the net.
Martin O'Neill made a triple substitution late on and two of the late arrivals made an immediate impact as Celtic added to their tally.
Ross Beattie picked up the ball on the left before picking out Maloney who buried it past Dubourdeau.
Killie's misery was completed in injury time when Sutton completed his hat-trick from the spot after Larsson was felled in the box by Freddie Dindeleux.
Kilmarnock: Dubourdeau, Shields, Greer, Hessey, Dindeleux,
McLaughlin, Fowler (Canero 45), Fulton, McDonald,
Di Giacomo (McSwegan 72), Invincibile (Nish 63).
Subs Not Used: Meldrum, Hardie.
Booked: Greer, Fulton, McSwegan.
Celtic: Hedman, Varga, Balde, McNamara, Miller,
Lennon (Wallace 81), Petrov, Gray (Sylla 81), Larsson, Sutton,
Hartson (Maloney 81).
Subs Not Used: Douglas, Valgaeren.
Ref: H Dallas