By Alex Livie
Last Updated: 01/01/70 1:00am
A hat-trick from Chris Sutton, a John Hartson header and a neat finish from Shaun Maloney sealed the victory for The Bhoys, who started the day with a five-point lead.
Killie had chances of their own, but ultimately failed to find a way past Magnus Hedman.
The deadlock was broken 21 minutes in when Sutton converted from the penalty spot after Stilian Petrov went tumbling in the box, with Killie unhappy with referee Hugh Dallas' decision to award the spot kick.
Goalmouth action was somewhat sporadic, with Greg Shields having Killie's best chance of the half when shooting narrowly wide, while Henrik Larsson hit a post seconds before the interval.
Greg McDonald forced Hedman into a fine save just after the hour, but Celtic used the scare as a spur and Liam Miller volleyed narrowly wide.
Minutes later the match was effectively ended as a contest when Hartson powered a header into the top corner after Sutton flicked the ball into his path.
Killie's vigour was knocked out by the second and Sutton tucked home from close range, following good work from Larsson, while Maloney netted a fourth five minutes from time.
Sutton capped a fine personal performance with a late fifth, his second penalty, to rub salt into Killie's wounds.
Rangers remain five points adrift of their Glasgow rivals after easing to a 3-1 win over Partick Thistle.
Mikel Arteta fired The Gers in front on eight minutes with a deft free kick and Alex McLeish's men moved into cruise control shortly before the interval when Michael Mols netted from close range.
Arteta grabbed his second of the game, from the penalty spot, on 77 minutes. Partick netted a late consolation through James Grady.
Hearts came from behind to beat Livingston 3-1 to cement their third place.
Derek Lilley gave Livi a 52nd minute lead, but strikes by Mark De Vries, Andy Kirk and a last minute Steven Pressley penalty sealed the three points for the capital club.
Dundee lost ground on Hearts after being held to a 1-1 draw by Hibernian. Nacho Novo gave Dundee a first half lead but they were denied the win when Derek Riordan scored ten minutes from time.
Motherwell heaped more pressure on Aberdeen with a 3-0 win at Pittodrie.
An early goal by Steven Craig stunned The Dons, who succumbed late on to goals from Stephen Pearson and Keith Lasley.
Strikes from Scott Thomson and Billy Mehmet gave Dunfermline a 2-0 win over Dundee United.