Match ends, Kilmarnock 0, Celtic 1.
An incredible last-minute strike from Tom Rogic gave Celtic a precious victory against Kilmarnock.
Both sides had chances to win with Killie's Kris Boyd testing keeper Craig Gordon and Celtic's Erik Sviatchenko having a header cleared off the line.
But it was disappointment in the end for Lee Clark, who had watched his struggling side defend valiantly.
And Rogic ensured Celtic go into the international break four points clear at the top of the Scottish Premiership.
Ronny Deila's side re-established a four-point gap over Aberdeen, who lost to Motherwell later on Saturday, with Celtic's next league game against Hearts on 2 April.
Both sides at Rugby Park were desperate for the three points, but for very different reasons.
Kilmarnock are eager not to be dragged into a relegation battle with Dundee United, who trail them by eight points ahead of their meeting with Dundee on Sunday, while Celtic are well aware of the Dons snapping at their heels in the title fight.
Celtic handed a first league start to Turkish forward Colin Kazim-Richards and Clark had to make do without his top scorer Josh Magennis, who rolled his ankle in training, and Steven Smith, who is out for the season.
The first real chance fell to Kilmarnock's Boyd, whose angled volley from a Kallum Higginbotham centre was blocked well by Gordon.
The visitors looked content to nibble away at a pretty solid home defence - Leigh Griffiths and Sviatchenko both watching headers flash wide.
Deila switched his formation to accommodate Kris Commons' replacement Patrick Roberts in the second half but Lee Hodson almost took advantage of some positional confusion in the Celtic midfield as he burst through to fire just past a post.
Denmark international Sviatchenko thought he had broken the deadlock with a header from Roberts' corner only to be foiled by Julien Faubert's alertness on the line.
As the clock continued to count, down the frustration among the Celtic fans grew louder.
Needless mistakes at the back fed that as Dedryck Boyata - who replaced the injured Kieran Tierney in the first half - was caught badly to allow Gary Dicker an unchallenged shot, but the midfielder's effort was wayward.
Late rally delivers for Deila
Kazim-Richards had a speculative shot with 10 minutes to go but it was weak and reflected his afternoon's performance.
Top scorer Griffiths almost snatched victory at the end but his curved strike sailed wide.
And just as a draw looked inevitable, Nir Bitton's replacement Rogic sent a thunderous 25-yard shot past Jamie MacDonald to send the Celtic fans falling over each other in delight behind the Kilmarnock goal.
- 27HodsonBooked at 67mins
- 7McKenzieSubstituted forSplaineat 55'minutes
- 9BoydSubstituted forObadeyiat 70'minutes
- 63TierneySubstituted forBoyataat 41'minutes
- 42McGregorBooked at 72mins
- 15CommonsSubstituted forRobertsat 45'minutes
- 6BittonSubstituted forRogicat 79'minutesBooked at 90mins
- 9GriffithsBooked at 67mins
- Alan Muir
- Shots on Target
Second Half ends, Kilmarnock 0, Celtic 1.
Scott Brown (Celtic) wins a free kick in the attacking half.
Foul by Aaron Splaine (Kilmarnock).
Tomas Rogic (Celtic) is shown the yellow card for excessive celebration.
Goal! Kilmarnock 0, Celtic 1. Tomas Rogic (Celtic) left footed shot from outside the box to the top left corner. Assisted by Patrick Roberts.
Attempt missed. Aaron Splaine (Kilmarnock) right footed shot from the centre of the box is close, but misses to the right.
Attempt missed. Leigh Griffiths (Celtic) left footed shot from outside the box is close, but misses to the left.
Attempt saved. Aaron Splaine (Kilmarnock) right footed shot from outside the box is saved in the bottom right corner.
Attempt saved. Colin Kazim-Richards (Celtic) right footed shot from outside the box is saved in the centre of the goal.
Substitution, Celtic. Tomas Rogic replaces Nir Bitton.
Colin Kazim-Richards (Celtic) wins a free kick in the attacking half.
Foul by Lee Ashcroft (Kilmarnock).
Attempt saved. Gary Dicker (Kilmarnock) right footed shot from outside the box is saved in the top centre of the goal.
Callum McGregor (Celtic) is shown the yellow card for a bad foul.
Foul by Callum McGregor (Celtic).
Julien Faubert (Kilmarnock) wins a free kick in the attacking half.
Attempt missed. Tope Obadeyi (Kilmarnock) right footed shot from outside the box is close, but misses to the left.
Substitution, Kilmarnock. Tope Obadeyi replaces Kris Boyd.
(Celtic) wins a free kick in the attacking half.