Julian Alvarez's wonderful curling strike sealed the three points for Man City in the final five minutes, after the hosts had equalised against the run of play early in the second half through Lois Openda.
Jeremy Doku made absolutely sure of the win when he scored his first Champions League goal on the break in injury time with Leipzig throwing everybody forward.
Phil Foden was involved in almost everything on the night for City, and it was his goal that gave Pep Guardiola's side the lead early on.
The results marks back-to-back victories to start the group for City, ahead of a double-header against Young Boys after the international break.
After Erling Haaland netted five goals in this fixture back in March, when City rampaged to a 7-0 win, the Norwegian frontman was a little more quiet in the first half.
Foden was central to everything good about City in the opening 45 minutes, and it was his shot-cum-cross that presented the visitors with their first clear opening, but Bernardo Silva failed to make contact with the ball.
Just moments later, it was Foden himself who took the shot on, jinxing past three defenders after Yussuf Poulsen conceded possession in his own area, but the effort was sliced wide of the keeper's left-hand post.
The England international would soon get his reward for his good first-half work though, when he latched onto Rico Lewis's pull back, and despite screwing his effort into the ground, his strike left Janis Blashwich helpless.
It was all City in the first half, with the visitors dominating territorially and in possession, as Leipzig would have been more than happy to go in only one-nil down.
Remaining in sight proved crucial too, as with just their second shot of the evening, Leipzig found themselves level.
After losing possession on the edge of the Leipzig area, City were wide open defensively, and Poulsen was able to feed Openda, who shrugged off the challenge of Manuel Akanji and fire home off the inside of the far post.
The game fell back into a familiar pattern after the goal though, with Guardiola's side continuing to have all of the ball, and Foden remaining influential.
It was a low Foden cross, fizzed in low to the back post, which brought about Haaland's first chance of the evening, and even though he was on the stretch, the City forward would have been disappointed to miss the target with the goal gaping.
Foden once more went close for the Premier League side, striking the underside of the crossbar from a very acute free kick with Blaswich swamped inside his own six-yard box.
However, the clinical moment finally came as substitutes Doku and Alvarez linked up, and the Argentine picked out the top corner with a phenomenal curling strike which left Blaswich well beaten.
Leipzig instantly came out of their shell and threw the kitchen sink at City, and that proved costly on the break, as Alvarez returned the favour, feeding Doku, who raced through on goal and coolly slotted past the Leipzig keeper to seal the three points.
It was no less than what City deserved, as their dominance in possession and in attack was eventually rewarded, even if they made their supporters wait.
City have another important encounter on the road at the weekend when they travel to the Emirates to face Arsenal on Sunday.
Leipzig welcome early-season strugglers Bochum to the Red Bull Arena at the weekend, and are at home once more on matchday three when Red Star Belgrade visit from Serbia.