Despite the scoreline, Kilmarnock put up some stern resistance at Parkhead, although Celtic ran out 5-1 winners.
Level at half-time, the Rugby Park side must have fancied their chances of at least a share of the points.
That was before Celtic steamrollered over them with a five-goal second-half blitz.
Didier Agathe was the player who surprisingly made the breakthrough for the home team with only his second league goal of the season before the established duo of John Hartson and Henrik Larsson made their contribution.
Stephen Pearson added a fourth with a clinical finish before Eric Skora, on loan from Preston until the end of the season, netted what was probably the best goal of the afternoon with a delicate chip from 20 yards.
Hartson rounded off the scoring with a close-range header as Celtic swept aside the opposition in pursuit of a league title which looks destined for Parkhead.
It was hard to remember, but Killie had competed as well as any side at Parkhead this season, at least in the first half.
The visitors looked composed early on with ex-Ranger Gary McSwegan unfortunately mis-hitting his shot from a half chance created by Danny Invincibile.
Pearson then showed up well with a dangerous run into the box before Larsson nearly put Celtic ahead.
A sweeping move involving Neil Lennon, John Kennedy and Chris Sutton ended with the Swedish striker watching a powerful left-foot shot on the turn being touched over the bar by Francois Dubourdeau in the Kilmarnock goal.
Invincibile tested Rab Douglas with a snap shot which the Celtic keeper did well to get down to and hold.
The home team started to crank up the pressure and Pearson's flashing header from an Agathe cross was not far off target.
Sutton went even closer a minute later when his back post header from a delicate Pearson cross came back off the underside of the bar after a slight deflection from Garry Hay.
The home crowd though the breakthrough had arrived when Jackie McNamara released Pearson with a clever pass down the left flank and from his cut back, Hartson looked as though he must score before mis-hitting his shot straight at Dubourdeau.
McNamara then came to his side's rescue with a well -timed tackle on Gary McSwegan after Kennedy had carelessly conceded possession to Skora.
Invincibile wasted a good chance for the visitors just before half-time when McSwegan's cross reached him at the back post, but the Aussie's effort lacked conviction and drifted wide.
Celtic piled on the pressure after the break and Kilmarnock's resistance was finally breached with a well taken goal.
Agathe powered his way down the wing before playing a one-two with Hartson which ended with his shot high into the roof of the net.
As Celtic boss Martin O'Neill said afterwards: "The goal gave him confidence and for a 15 to 20 minute spell he was the Didier of old. He was explosive.
"The crowd can get impatient with wide players if they are not beating three or four players every time, but we need width at all times, especially here at Parkhead. I am delighted with him." Douglas saved well from McSwegan after a poor clearance by Kennedy before Celtic got their second.
Agathe's pace took him past Hay before Hartson's strength enabled him to hold off David Lilley's challenge as he headed home.
Larsson, who has been fairly subdued all afternoon by the excellent Gordon Greer, then contributed a third with a neat shot on the turn after Agathe had again created the chance.
When Pearson slid the ball home under Dubourdeau after Lennon's pass split the visitors' defence wide open, it really was cruel on Killie.
Substitute Kris Boyd found Skora and the Frenchman scored with a superb chip from outside the box which left Douglas grabbing thin air to at least give Kilmarnock some consolation.
There was still time for substitute Shaun Maloney to find Hartson with a cross which the Welsh striker headed home with ease before it was all over.
Afterwards, O'Neill was effusive in his praise of Lennon amongst others.
"He's having a great time and has been one of our most consistent players all season along with Chris Sutton and Stan Varga." For Jim Jefferies it was a desperately disappointing afternoon.
"It's the best we've played at Parkhead since I came here, especially in the first half.
"We had the best two chances in that first half, but Celtic scored with every chance that they had in the second. I'm pleased with a lot of our play though our last half-hour was disastrous." Man of the match: Neil Lennon - The midfield player patrolled his beat with power and purpose and drove on his team-mates when things were not going for them, especially in the first half.