Youssouf Mulumbu’s first goal for Kilmarnock condemned Celtic to only their second domestic defeat under Brendan Rodgers.
The midfielder scored in the second half to deliver the reward for the home side’s disciplined display.
Mulumbu should have scored again late on, but Dorus de Vries saved.
Celtic not only failed to score, but failed to land a shot on target until the last minute, and lost Dedryck Boyata and Kristoffer Ajer to injury.
The win, Kilmarnock’s fifth in a row at home, moved the Rugby Park side into the top six.
Rodgers’ side took to the pitch in Ayrshire knowing a victory would give them four straight wins for the first time this season.
Relatively speaking, the champions had been looking stodgy before the winter break, but the new year had been offering evidence of a fresh spark.
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There was an immediate debut for the former Dundee defender Jack Hendry, who joined late in the transfer window, but his importance to the visiting defence couldn’t have been predicted.
He very quickly went from new boy to main man as both his defensive partners were forced off in the first half through injury.
It took just 10 minutes for Boyata to suffer a knock and limp off in frustration.
Ten minutes before the break, Ajer joined him on the sidelines after picking up an ankle injury. Nir Bitton and Scott Sinclair replaced them in a well-shuffled pack.
Against a Kilmarnock side bursting with Steve Clarke-injected confidence, the champions started well.
Olivier Ntcham tried his luck from range and Charly Musonda looked ready to open his box of tricks playing just behind Moussa Dembele up front.
But the home side stood firm in the face of a potential storm that quickly came to not very much.
Snuffing them out was a group of Kilmarnock players who were snapping at every heel and chasing every lost cause.
Their work rate was impressive but they also threatened.
Kirk Broadfoot watched a header fly just over, and both Greg Taylor and Kris Boyd both had shots saved before the break. They sensed a nervousness in the makeshift Celtic defence and they were making it creak.
As Celtic tried to force the issue more in the second half, the home side continued to frustrate.
Dembele, Sinclair and Musonda were given no room to breathe in the danger areas and were limited to half chances on what was increasing looking like a very sticky surface.
But Clarke’s side were growing in assurance and it came as no real surprise when they took the lead with 20 minutes to go.
Jordan Jones, who had another excellent 90 minutes, picked the ball up on the left and picked out an unmarked Mulumbu at the back post, who was left with a simple finish.
