- Kyogo Furuhashi (45'+2')
The defeat, Rangers' second in four games already this season, leaves them fourth.
Kyogo Furuhashi's goal in first-half stoppage time was enough to settle the tie in Celtic's favour and give them the early-season bragging rights.
But Rangers had already had the ball in the back of the net twice before that. Rabbi Matondo saw his effort ruled out for offside while Kemar Roofe controversially had a goal disallowed by the VAR for a foul on Gustaf Lagerbielke.
Celtic goalkeeper Joe Hart was called upon to keep the visitors in front several times in the second-half but Brendan Rodgers' side stood firm to claim an important victory.
The defeat, which comes on the back of Rangers' Champions League elimination against PSV Eindhoven in midweek, will increase the pressure on manager Michael Beale to mount a title challenge.
- Don Robertson