The champions went into the game as the bookmakers' underdogs but belied the odds by comfortably holding off their rivals following Odsonne Edouard's opener.
The Hoops now have a perfect record from four games with Rangers in the position of chasing their city rivals again.
Here, the PA news agency looks at five other things we learned from the weekend's action.
1. Celtic's new defenders can handle the heat
Rangers midfielder Steven Davis admitted they felt they could exploit Celtic's inexperience as three of their back four made their Old Firm debuts, but Fraser Forster was relatively untroubled in the visitors' goal. Christopher Jullien picked up man of the match after his best display in a Celtic shirt, Boli Bolingoli encountered few problems despite some sloppy passing, and Hatem Abd Elhamed performed brilliantly considering he has been suffering from a hairline fracture in his side. Another debutant, Moritz Bauer, came on and helped keep a clean sheet after the impressive Nir Bitton limped off.
2. Celtic can mix it up
Neil Lennon instructed his side to play in the Rangers half after losing an early goal on their previous visit after trying to play the ball out from the back. The tactic was evident from the first whistle as they kicked the ball out deep in home territory. Allowing Ryan Christie, Mikey Johnston and Callum McGregor to get on the ball in the opposition half helped keep Rangers at bay.
3. Rangers still have work to do
Steven Gerrard's men lacked creativity and tempo in the final third while wide players Sheyi Ojo and Jordan Jones made a limited impact when brought on in a bid to change the game. Celtic took their goal tally for the season to 41 and look like they will keep scoring in every game.
4. There's trouble brewing in the capital
Hearts manager Craig Levein and Hibernian head coach Paul Heckingottom incurred the wrath of their respective fans following disappointing results. Heckingbottom admitted his side were too soft as they went down 3-0 to Motherwell while Levein criticised his team's defending in a 2-2 home draw with Hamilton. Both bosses were bullish after the games as they insisted their teams would improve.
5. Gary Holt is on the mend
The Livingston manager was absent from training late last week and their game against St Mirren after being hospitalised, but he was in touch with assistant Davie Martindale to offer congratulations on their 2-1 home win over Livingston and is expected to be back at work soon.