First half goals from Kemar Roofe and Alfredo Morelos, either side of Odsonne Edouard’s header gave the hosts the half-time lead – and the y capitalised on Celtic’s ten men to add another through Roofe in the second half.
Roofe's first - a clever chested finish from ten yards out to beat Scott Bain - was followed immediately by Callum McGregor's dismissal for Celtic after picking up a second yellow card in the build-up.
Celtic responded when Edouard headed in from close range but Morelos was emphatic in his finish to restore the lead Rangers would not relinquish.
Roofe added a classy header in the second to extend the lead, but Borna Barisic limped out with 15 minutes left to slightly sour an enjoyable afternoon for the blue half of Glasgow.
Substitute Jermain Defoe added a late goal to add gloss to the scoreline.
Here is how the Rangers players rated in the victory.
Player ratings scale - 10: One of best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: Terrible day at office. 2: Abysmal. 1: One of worst performances you've seen.
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5. Jack Simpson - 5
Caught flat-footed and outjumped by Ajer at Celtic equaliser. Harshly cautioned early on which made Ol Firm debut even more difficult. Photo: Ian MacNicol
6. Glen Kamara - 7
Took everything in his stride and kept the ball moving all over the park but found himself in space frequently in advanced areas. Photo: Craig Foy - SNS Group
7. Steven Davis - 8
Afforded more space once McGregor was sent off and assumed control of the game from that point. Photo: Rob Casey - SNS Group
8. Joe Aribo - 7
Breezed through the game but never off the pace. Eased into possession and second balls to exhibit footwork and control that was a nightmare for opposition. Photo: Rob Casey - SNS Group