Leigh Griffiths was the hero as he scored in the 89th minute to give 10-man Celtic a massive win after a poor performance.
The opening 45 minutes were fairly dull as both sides created chances but none were clear-cut.
Callum McGregor had the best chance as he fired his shot just wide of the post after a good run from Stefan Johansen from midfield.
Kris Commons returned after missing the trip to Hearts with an ankle injury and had a shot inside the area blocked but looked off the pace of the game.
Nadir Ciftci had one effort on goal and was replaced at half-time by Leigh Griffiths who made an instant impact for Celtic.