Celtic produced a classy second-half display to reinforce manager Neil Lennon's assertion their focus would now be the Scottish Premier League after their Champions League progress.
Adam Matthews' run and cut-back set up Scott Brown for Celtic's opener.
Kilmarnock's Paul Heffernan had a great chance blocked after the restart.
But Joe Ledley slid in at the back post to convert a Brown pass and Georgios Samaras headed a third before Cillian Sheridan scored a late goal for Killie.
Despite Kilmarnock manager Kenny Shiels' warning that he would defy a Scottish Football Association ban and play his captain, there was no sign of defender Manuel Pascali as he served the second of his two-game suspension.
Celtic had their skipper in action, as Brown continued to postpone hip surgery.
However, they were without two of their heroes from their midweek Champions League win over Spartak Moscow as Kris Commons was ruled out with a badly-bruised dead leg and Samaras started on the bench.
Celtic took the lead with a well-worked goal down the right wing after 27 minutes, Brown side-footing Adam Matthews' cut-back into the net after the Welshman's foray forward had been rewarded by Gary Hooper's clever pass.
Cillian Sheridan caused Celtic goalkeeper Fraser Forster a minor flutter when he arrowed a left-foot shot over the bar from 22 yards and there was further consternation for the visitors when Liam Kelly's curling shot drifted a fraction wide.
Shiels' half-time team talk spurred Kilmarnock into an immediate attack at the restart.
Kelly advanced unchallenged down the left wing and swung in a delightful ball for Heffernan, who brought it down and took an extra touch before slamming a shot at goal that Charlie Mulgrew blocked brilliantly.
Within seconds, Matthews was off and running down the right flank and, in a similar move to the opening goal, he cut the ball back for Hooper who thundered a shot that Cammy Bell saved sharply to his left.
Black-shirted Celtic continued in this mode and might have been further ahead had the home defence not been so brave or well-organised.
Centre-half Michael Nelson was a key figure in that regard and he smothered a fierce effort by Nouinoui Lassad after Joe Ledley had fed Emilio Izaguirre who crossed into the box.
Killie had Gary Harkins and Heffernan offering moments of brightness but with 25 minutes to go Celtic scored their second.
Victor Wanyama slid a ball to Brown inside the box and his low cross was converted by the Welsh midfielder Ledley.
As Celtic turned on the style, Wanyama had a low shot saved by Bell but there was further pain for the home fans when Matthews created Celtic's third.
This time it was Brown who sent him scurrying down the right and his lofted cross to the back post was headed in off the crossbar by substitute Samaras for his seventh goal of the season.
With two minutes to go Efe Ambrose headed wide of the target when he really ought to have converted Mulgrew's curling free-kick.
Sheridan volleyed Jeroen Tesselaar's cross past Forster for a late consolation but the overall impression is of a Celtic side with renewed appetite for domestic competition now they have emerged from Champions League Group G.
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