Goals from Cillian Sheridan and Liam Kelly saw Kilmarnock claim their first league victory over Celtic in Glasgow since 1955.
The Hoops suffered their first home defeat of the season after having put in a brave performance against Barcelona in the Champions League on Tuesday night.
The home side made numerous changes with Adam Matthews, James Forrest, Beram Kayal, Kris Commons and Miku all coming in for starts. Opposition boss Kenny Shiels, meanwhile, handed a first start to 17-year-old defender Mark O’Hara.
Both sides started slowly, with the only chances coming the way of Rory McKeown for Kilmarnock, then Forrest for Celtic, but both Fraser Forster and Cammy Bell in the respective goals weren’t called into action.
Celtic started to gain control over the game, with Emilio Izaguirre crossing for Miku, but before the striker could get a shot off Kelly dived in to divert the ball away for a corner.
The best chance of the first half for the home side came when Commons crossed from the left to Miku and he headed the ball onto Joe Ledley, but the midfielder out could only fire the ball over the bar from six yards.
Neil Lennon’s side continued to press forward, with Forrest firing in a cross which Miku only just failed to reach at a stretch.
Just before the break Kilmarnock went into a shock lead as a slack pass from Matthews towards Efe Ambrose saw the towering defender robbed by Sheridan and the former Celtic youngster made no mistake, rounding Forster and tapping the ball into the net.
Hoops gaffer Lennon was clearly upset with his side and brought on striker Gary Hooper in place of the ineffective Kayal. The English forward almost got his side level when he got onto a cross from the right by Forrest, but he could only divert it wide of Bell’s left hand post.
But, on the hour mark, the visitors went two ahead as Rory McKenzie was brought down on the edge of the area by Izaguirre, leading the referee to point to the spot and allowing Kelly to fire a penalty past Forster.
The home side had two glorious chances to get back into the game, with firstly Izaguirre being called offside after a pass from substitute Paddy McCourt, then Tony Watt smashing the ball from a Forrest cross over.
But the visitors managed to hang on and claim a famous victory over the league leaders.