Match ends, Kilmarnock 0, Celtic 1.
Stuart Armstrong's first-half goal was enough to guide Celtic past Kilmarnock and stretch their lead to 13 points at the top of the Scottish Premiership.
Armstrong powered onto Moussa Dembele's through-ball and slotted past Jamie MacDonald a minute before the interval.
Mikael Lustig's drive struck the outside of Jamie MacDonald's post after the break, with Lee Clark's industrious hosts struggling to carve out clear-cut opportunities.
Killie remain seventh in the table.
Celtic's green and white hoops made way for third-strip pink on a freezing cold night in Ayrshire and there were plenty of personnel changes too for both sides.
The last man to score domestically against Celtic, Souleymane Coulibaly, started on the bench as Kilmarnock boss Clark decided to take a more "pragmatic" approach to his team selection.
The 6-1 thumping they suffered the last time the two sides met perhaps helping to focus the mind. The Albanian striker, Flo Bojaj, was tasked with leading the line.
Two of Celtic's changes were at the back, where Dedryck Boyata made his first start under Brendan Rodgers. Callum McGregor provided the left-back cover in the absence of Kieran Tierney and Emilio Izaguirre.
The most notable absentee was up-front, however, with striker Leigh Griffiths suffering from "tightness in his hamstring" after Scotland's 3-0 defeat to England last Friday.
The visitors started by knocking the ball around with the swagger of an unbeaten side well clear of their domestic rivals.
However, Kilmarnock started to find their feet and looked increasingly threatening down the left, where Greg Taylor was enjoying plenty of possession.
As ever, though, when Celtic poured forward, they looked dangerous. Erik Sviatchenko watched his diving header drift just over the bar and MacDonald provided a spectacular save when James Forrest's curling effort looked destined for the top corner.
As chances came and went, the home side grew in confidence, but as they headed towards the break with their tails firmly in the air, Armstrong got the break of the ball from Dembele's stab through and provided the sucker-punch with a close-range shot that flew past McDonald.
When McGregor had an early chance saved in the second half, it looked as if Celtic might well find another gear and put the game to bed, but Kilmarnock were having none of it.
The home side gave everything and pushed a sloppy Celtic all the way.
Boyata was forced to clear off the line and Adam Frizzell also came close.
As the clock ticked, Celtic pushed. Lustig hit the post, but the momentum was with Kilmarnock. They sensed an equaliser, but it didn't come and Celtic march on with yet another clean sheet.
Kilmarnock manager Lee Clark: : "I'm disappointed for the players - I thought they were terrific.
"I thought the game plan was really strong, defensively we've done great - one lapse and Celtic have scored.
"We grew into the game as an attacking force and second half we played a lot more on the front foot and created our own chances.
"If my players deliver that type of performance in the seven games in 28 days in December, we'll give ourselves a great opportunity to put ourselves in a good position in the league.
"Overall, my emotion is pride in my players' performance, because we were depleted."
Celtic manager Brendan Rodgers: "I thought first half we played very well. Our patience and quality on a difficult surface was good. We created some chances; it took us a bit of time until we got the goal, and it was a great finish from Stuart (Armstrong).
"At 1-0, you have to ensure you're defensively strong and we were.
"We gave away a couple of needless free kicks, and need to manage that side a bit better, but in the main it was a great victory for us on the back of an international break, on astroturf, in what is a difficult place."
- 8DickerBooked at 63minsSubstituted forMcFadzeanat 89'minutes
- 3SmithBooked at 75mins
- 11JonesSubstituted forCoulibalyat 78'minutes
- 20BojajSubstituted forTysonat 58'minutes
- 27RobertsSubstituted forRogicat 66'minutes
- 8BrownBooked at 90mins
- 14S ArmstrongBooked at 72mins
- 49ForrestSubstituted forBittonat 85'minutes
- 11SinclairBooked at 41mins
- 2K Touré
- 24de Vries
- Don Robertson
- Shots on Target
Second Half ends, Kilmarnock 0, Celtic 1.
Foul by Nathan Tyson (Kilmarnock).
Mikael Lustig (Celtic) wins a free kick in the defensive half.
Corner, Celtic. Conceded by Rory McKenzie.
Scott Brown (Celtic) is shown the yellow card for a bad foul.
Greg Taylor (Kilmarnock) wins a free kick in the defensive half.
Foul by Scott Brown (Celtic).
Substitution, Kilmarnock. Callum McFadzean replaces Gary Dicker.
Attempt saved. Tomas Rogic (Celtic) left footed shot from outside the box is saved in the bottom right corner.
Foul by Adam Frizzell (Kilmarnock).
Scott Brown (Celtic) wins a free kick on the right wing.
Nathan Tyson (Kilmarnock) wins a free kick in the defensive half.
Foul by Erik Sviatchenko (Celtic).
Substitution, Celtic. Nir Bitton replaces James Forrest.
Corner, Kilmarnock. Conceded by Dedryck Boyata.
Attempt blocked. Gary Dicker (Kilmarnock) header from the centre of the box is blocked.
Rory McKenzie (Kilmarnock) wins a free kick in the defensive half.
Foul by Scott Brown (Celtic).
Souleymane Coulibaly (Kilmarnock) wins a free kick in the defensive half.