Filip Helander’s goal was the difference, the Swede rising highest to meet Borna Barisic's corner in the second half.
Celtic started well but lost their control after the interval and struggled to test Robby McCrorie until they fell behind.
There were a number of poor performers for the visitors and Ange Postecoglou's men have started the season with the fewest number of points since the 90s. They find themselves sixth with six points after four games going into the international break.
How did the 15 players involved rate out of ten?
Player ratings scale - 10: One of the best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen.
5. Josip Juranovic - 6
Played out of position at right-back and looked uncomfortable at times as he cut on to his stronger foot. Didn't do much wrong against Joe Aribo. Photo: Rob Casey - SNS Group
6. Callum McGregor - 6
A game of two halves for the Celtic captain. Such a calm and composed presence at the base of the Celtic midfield in the first half. Took the ball under pressure and performed a real captain’s role, advising his team-mates where they needed to be for the team. Rangers nullified him after the break and Celtic's control diminished. Photo: Rob Casey - SNS Group
7. David Turnbull - 5
In the first half played some excellent penetrative passes to break the lines or allow Celtic to get in behind the Rangers defence. But he wasn't on the ball enough and completely fell out of the game before being subbed in the second half. Photo: Rob Casey - SNS Group
8. Ryan Christie - 4
Not on it at all at any time in the game. Frustrated Kyogo Furuhashi in the first half when he opted to shoot rather than play a 1-2. Was guilty of giving the ball away cheaply. Photo: Craig Foy - SNS Group