A goal from their number five with 67 minutes played on the day they marked the death of Billy McNeill moved Celtic to within a point of the Scottish Premiership title.
Jozo Simunovic headed in wearing the jersey graced by the Lisbon Lion and former manager, who died on Monday.
Celtic started briskly, having taken part in wreath laying before kick-off.
But goalkeeper Scott Bain had to deny Kilmarnock on several occasions before Celtic eked out a narrow victory.
Rangers must now beat Aberdeen at Ibrox on Sunday to delay their city rivals earning an eighth successive championship.
Celtic are now unbeaten in 15 Premiership games but were made to work hard for their win against a makeshift Kilmarnock side shorn of three first-team regulars through suspension.
Display fails to match classy tributes
All week, the Celtic fans had mourned and celebrated their ultimate hero and that huge appreciation of the life and times of the great man swept across the stadium like a giant wave.
A huge number five bedecked the centre circle and the players’ black armbands, the surviving members of the 1967 European Cup-winning team were brought on to the pitch, there were songs and flags and 67 seconds of applause. It was a classy farewell, the kind of send-off that demanded a dominant display in its wake. And that’s where Celtic’s problems began.
Through suspension and injury, Kilmarnock were missing three defenders, not that you would have noticed. Gary Dicker and Alex Bruce were deposited in the heart of the defence and were excellent. Stephen O’Donnell was high-energy alongside them. In front, Alan Power was alert and influential and, further on, the visitors had pace and wit through Chris Burke, Liam Millar and Eamonn Brophy.
Celtic had little zip about them in the opening half. Their tempo was slow, their urgency and accuracy nowhere near what the crowd was looking for on this day of all days. You expected the emotion of the day to produce a powerhouse performance, but they haven’t been delivering that kind of excellence for quite a while now.
They dug it out in the end after an improved second half. The winner came after 67 minutes – spooky enough – and 16 seconds through a header from a centre-half wearing the number five that McNeill once wore. Spookier still.
The points were precious, but this was another below-par Celtic day in a growing list of below-par Celtic days. Little of what happened here will have added ballast to Neil Lennon’s prospects of being the permanent manager in the summer.
Bottom line, it was a win, but the visitors made it nervous to the last kick. Kilmarnock should have been ahead at the break. Three minutes after a penalty shout when O’Donnell was challenged by Scott Brown, Burke got a lucky break of the ball in the Celtic penalty area and a bit more decisiveness in his finish was required. One-on-one with Bain, his attempt was too tame. It was a golden chance.
Three minutes later, Kilmarnock cut through again, Millar breaking away from James Forrest and Mikael Lustig down the left only to shoot straight at Bain from the angle. Directly after, Conor McAleny fired on goal, Bain tipping it over for a corner.
A fourth attacking moment came within minutes, Kristoffer Ajer losing control of the ball in front of his own box and getting ransacked by Brophy. It was only the defender’s pace to put a tackle in on the striker that dug him out of a hole.
Invaluable goal in different ways
None of this was doing Lennon’s chances of getting the Celtic job on a permanent basis any good. The beginning of the new half saw Kilmarnock continue their threat, Brophy and Burke testing Bain.
Celtic had to get their act together sooner or later and the first suggestion that they were about to climb from their torpor was an Odsonne Edouard effort that curled just wide of Daniel Bachmann’s goal.
Bachmann was pressed into action again within seconds, denying Callum McGregor and Edouard in a mad flurry. Kilmarnock were defending much deeper now. Celtic were beginning to carry that menace you thought would be there from the get-go.
A brilliant piece of defending kept Edouard out just after the hour, but the defensive stand was about to crack. Simunovic soared above Aaron Tshibola and nutted home at the back post to bring joy, but mostly relief, to Celtic Park.
The goal was invaluable not just because of the importance of the three points in the context of wrapping up the league title sooner rather than later, but because of their desperation to do justice to this emotional occasion with a victory rather than a deflating draw, or worse.
Celtic did enough, just. They were nervous and inaccurate for much of it against a sprightly team that will feel unfortunate not to get something from their day.
The big number five in the middle of the Celtic defence made sure they got nothing. How many times has that been said in their distant and more glorious past?