The game started very even, with neither side truly dominating the opening stages.
The home side had a chance from a corner after eight minutes, but Celtic's defence did well to clear their lines at the back post.
Anthony Stokes came close for Celtic with a free kick on 14 minutes, but his effort went just past the post.
Celtic began to get on top and took the lead after 33 minutes when Georgios Samaras headed home from a corner to make it 1-0.
Teemu Pukki almost doubled the away side's lead two minutes later, but saw his shot deflected wide.