Jack Grealish got off to a dream start in his very first Champions League game with an assist in the first half at the Etihad.
The £ 100million man was named in Man City’s starting lineup to face RB Leipzig and immediately seized his opportunity.
His corner was greeted by a header from Nathan Ake, who nodded after 16 minutes, to secure a first assist for Grealish.
It was also a first Champions League goal for the defender, who started in the absence of John Stones and Aymeric Laporte.
City were gifted with a second after 28 minutes thanks to a bizarre own goal.
De Bruyne found space on the right and whipped up a low, bouncy cross. Nordi Mukiele seemed to have covered him, but he only managed to catch Gulacsi on the wrong foot as he tried to send him back to the keeper.
Gulacsi could only watch as he bounced past him into the net.
Leipzig had a good fate and scored a goal after 42 minutes.
Emil Forsberg picked Mukiele with a deep cross and he redeemed himself for his previous mistake by coming back through the goal to prepare Christopher Nkunku to return home.
City were then able to restore their two-goal advantage, when Riyad Mahrez scored from the penalty spot.
A VAR incident saw the referee point straight ahead and Mahrez, who had missed five of his last nine, was right.
City entered the 3-1 break in their first Champions League game of the season.