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.
Live text and stats
Saturday, 8 December 2012
Scottish Premier League
07 Racchi (Sissoko 56)
08 Kelly yellow card
11 Harkins yellow card (McKenzie 68)
14 Heffernan yellow card
15 Perez (O'Hara 68)
01 Forster yellow card
03 Izaguirre (Kayal 76)
08 Brown yellow card
11 Nouioui (Samaras 66)
88 Hooper (Miku 82)
Ref: Craig ThomsonAtt: 6,501
Attempts on target
Attempts off target
90:00+2:05 The referee brings the game to a close.
90:00+1:03 Booking Fraser Forster booked for time wasting.
90:00+0:25 Assist by Jeroen Tesselaar.
90:00+0:25 GOAL - Cillian Sheridan:Kilmarnock 1 - 3 Celtic Cillian Sheridan gets on the score sheet with a goal from close range to the bottom left corner of the goal. Kilmarnock 1-3
88:24 Foul by Mark O'Hara on Charlie Mulgrew, free kick awarded. Charlie Mulgrew delivers the ball, Headed effort from deep inside
the area by Efe Ambrose misses to the right of the goal.
87:45 Free kick crossed right-footed by Liam Kelly from left channel.
87:45 Booking Scott Brown receives a caution for unsporting behaviour.
87:28 Scott Brown concedes a free kick for a foul on Cillian Sheridan.
85:18 Inswinging corner taken from the right by-line by Charlie Mulgrew, Cameron Bell makes a comfortable save.
84:37 Georgios Samaras is ruled offside. James Fowler takes the indirect free kick.
83:25 Victor Wanyama concedes a free kick for a foul on Mohamadou Sissoko. Free kick taken by Jeroen Tesselaar.
82:00 Outswinging corner taken right-footed by Liam Kelly, Ryan O'Leary has a header from close in and clears the crossbar.
81:18 Substitution Gary Hooper leaves the field to be replaced by Nicolas Fedor Miku.
79:07 Inswinging corner taken by Rory McKenzie from the left by-line, save by Fraser Forster.
78:13 Shot from just outside the box by Beram Kayal goes over the bar.
75:30 Free kick taken by Efe Ambrose.
75:30 Substitution (Celtic) makes a substitution, with Beram Kayal coming on for Emilio Izaguirre.
75:30 Paul Heffernan concedes a free kick for a foul on Scott Brown.
75:07 Foul by Scott Brown on Mohamadou Sissoko, free kick awarded. Mohamadou Sissoko takes the free kick.
73:27 Assist by Adam Matthews.
73:27 GOAL - Georgios Samaras:Kilmarnock 0 - 3 Celtic Georgios Samaras finds the back of the net with a headed goal from close range. Kilmarnock 0-3 Celtic.
71:12 Victor Wanyama takes a shot. Save by Cameron Bell.
71:04 Outswinging corner taken left-footed by Charlie Mulgrew from the left by-line.
70:26 Outswinging corner taken by Charlie Mulgrew from the left by-line.
Correction - 67:16 Substitution (Kilmarnock) makes a substitution, with Mark O'Hara coming on for Borja Perez.
Correction - 67:16 Substitution Rory McKenzie comes on in place of Gary Harkins.
67:16 Substitution (Kilmarnock) makes a substitution, with Mark O'Hara coming on for Borja Perez.
67:16 Substitution James Dayton on for Gary Harkins.
66:53 Corner taken by Borja Perez from the left by-line, Victor Wanyama manages to make a clearance.
66:41 Gary Harkins has a drilled shot. Kelvin Wilson gets a block in.
66:09 Booking The referee books Paul Heffernan for dissent.
65:34 Substitution Lassad Nouioui leaves the field to be replaced by Georgios Samaras.
64:45 Assist by Scott Brown.
64:45 GOAL - Joe Ledley:Kilmarnock 0 - 2 Celtic Joe Ledley scores a goal from close in to the bottom left corner of the goal. Kilmarnock 0-2 Celtic.
62:09 Inswinging corner taken by Borja Perez from the left by-line, clearance by Kelvin Wilson.
60:30 Outswinging corner taken by Charlie Mulgrew from the left by-line, clearance made by Ryan O'Leary.
60:20 The ball is swung over by Charlie Mulgrew, blocked by Ryan O'Leary.
57:53 Inswinging corner taken from the right by-line by Charlie Mulgrew.
57:01 Inswinging corner taken left-footed by Charlie Mulgrew, Victor Wanyama takes a shot. Clearance by Michael Nelson.
54:42 Fraser Forster takes the direct free kick.
54:42 Substitution (Kilmarnock) makes a substitution, with Mohamadou Sissoko coming on for Danny Racchi.
54:42 Booking Gary Harkins shown a yellow card.
54:37 Gary Harkins gives away a free kick for an unfair challenge on Scott Brown.
53:11 Foul by Cillian Sheridan on Efe Ambrose, free kick awarded. Efe Ambrose restarts play with the free kick.
52:23 Joe Ledley has shot on goal from just outside the area which goes wide of the right-hand upright.
49:54 Gary Harkins gives away a free kick for an unfair challenge on Victor Wanyama. Efe Ambrose takes the free kick.
49:38 Drilled right-footed shot by Victor Wanyama. Save made by Cameron Bell.
48:00 Corner taken by Charlie Mulgrew, Efe Ambrose produces a header from inside the area that goes over the bar.
47:21 Scott Brown fouled by Cillian Sheridan, the ref awards a free kick. Adam Matthews takes the direct free kick.
46:24 Corner taken by Charlie Mulgrew, Cillian Sheridan manages to make a clearance.
46:11 Drilled right-footed shot by Gary Hooper. Save made by Cameron Bell.
45:01 The referee starts the second half.
45:00+1:01 The ref blows to signal half-time.
45:00+0:36 Lassad Nouioui has an effort at goal from outside the box which goes wide left of the goal.
44:05 Unfair challenge on Cillian Sheridan by Efe Ambrose results in a free kick. Borja Perez delivers the ball from the free kick
right-footed from left channel, clearance by Charlie Mulgrew.
42:25 Lassad Nouioui is flagged offside by the assistant referee. Cameron Bell restarts play with the free kick.
41:53 Charlie Mulgrew takes the outswinging corner, clearance by Gary Harkins.
41:03 Free kick awarded for a foul by Borja Perez on Scott Brown. Victor Wanyama restarts play with the free kick.
38:06 Unfair challenge on Michael Nelson by Gary Hooper results in a free kick. Michael Nelson takes the free kick.
35:16 Cillian Sheridan produces a left-footed shot from outside the penalty box and misses left.
34:05 Adam Matthews takes a shot from just outside the penalty area which clears the crossbar.
33:35 Corner taken short by Charlie Mulgrew.
Correction - 32:34 Shot by Lassad Nouioui. Ryan O'Leary gets a block in. Corner taken left-footed by Charlie Mulgrew, clearance by Gary Harkins.
32:34 Shot by Lassad Nouioui. Blocked by Ryan O'Leary. Corner from left by-line taken by Charlie Mulgrew.
31:50 Free kick awarded for an unfair challenge on Paul Heffernan by Kelvin Wilson. Borja Perez restarts play with the free kick.
29:21 Free kick awarded for an unfair challenge on Ryan O'Leary by Efe Ambrose. Ryan O'Leary restarts play with the free kick.
28:09 Joe Ledley has an effort at goal from 20 yards. Save made by Cameron Bell.
Correction - 26:58 GOAL - Scott Brown:Kilmarnock 0 - 1 Celtic Scott Brown grabs a goal from inside the box to the bottom right corner of the goal. Kilmarnock 0-1 Celtic.
26:58 Assist by Adam Matthews.
26:58 GOAL - Scott Brown:Kilmarnock 0 - 1 Celtic Scott Brown finds the net with a goal from inside the penalty area to the bottom left corner of the goal. Kilmarnock 0-1 Celtic.
Correction - 25:38 Outswinging corner taken by Charlie Mulgrew, Efe Ambrose produces a header from deep inside the six-yard box that clears the
25:38 Corner taken by Charlie Mulgrew from the left by-line, Close range header by Efe Ambrose goes over the crossbar.
20:48 Charlie Mulgrew takes the direct free kick.
20:48 Booking Liam Kelly receives a caution for unsporting behaviour.
20:35 Liam Kelly gives away a free kick for an unfair challenge on Adam Matthews.
Correction - 18:51 Scott Brown fouled by James Fowler, the ref awards a free kick. Charlie Mulgrew delivers the ball from the free kick left-footed
from left channel.
18:51 Unfair challenge on Scott Brown by James Fowler results in a free kick. Charlie Mulgrew delivers the ball from the free kick
left-footed from left channel.
18:26 Effort on goal by Gary Hooper from 20 yards. Cameron Bell makes a comfortable save.
17:19 Foul by Scott Brown on Liam Kelly, free kick awarded. Free kick crossed right-footed by Borja Perez.
14:34 The ball is swung over by Danny Racchi, Kelvin Wilson manages to make a clearance.
13:40 Michael Nelson takes a shot. Save made by Fraser Forster.
12:52 Short corner taken by Borja Perez from the right by-line.
11:21 Victor Wanyama has an effort at goal from just outside the box which goes wide of the right-hand post.
9:20 Cillian Sheridan concedes a free kick for a foul on Charlie Mulgrew. Fraser Forster takes the direct free kick.
5:45 Victor Wanyama produces a right-footed shot from just outside the box that misses to the right of the net.
4:23 Unfair challenge on Scott Brown by Borja Perez results in a free kick. Direct free kick taken by Efe Ambrose.
3:45 The assistant referee signals for offside against Emilio Izaguirre. Cameron Bell takes the free kick.
0:38 Emilio Izaguirre sends in a cross, clearance made by Jeroen Tesselaar.
0:00 The match gets underway.
Live text and data provided by The Press Association.
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