Neither side were fully able dominate the opening stages, as they look to gain an early advantage.
Partick Thistle almost had a chance to take the lead on eight minutes, but Celtic cleared well at the back post.
Anthony Stokes came close with a free kick on 14 minutes, but his effort went just wide of the mark.
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.
Kallum Higginbotham had an ambitious effort on 53 minutes, but his chip from the edge of the area went just over the bar.
Partick struck an equaliser on 66 minutes, with Kris Doolan slotting home to make it 1-1.
Higginbotham forced his way through the Celtic defence on 73 minutes and forced a save from Forster with his effort on goal.
Two minutes later, Celtic regained the lead when Amido Balde went on a solo run before slotting under the goalkeeper to make it 2-1.
The Jags went in search of another equaliser and came close on 83 minutes through Sean Welsh, though Forster was on hand to keep out the effort.