Club-record signing Grealish made his European debut a memorable one on Wednesday, adding to an early assist for Nathan Ake with a sublime second-half strike.
City – in action in this competition for the first time since last season's final defeat to Chelsea – wobbled a little between those two efforts, benefitting from Nordi Mukiele's own goal and a Riyad Mahrez penalty but conceding twice to Christopher Nkunku.
Even after Grealish's goal, Nkunku's hat-trick strike caused further concern, only for Joao Cancelo and substitute Gabriel Jesus to notch numbers five and six for City and clinch three vital points in a tough Group A that also features Paris Saint-Germain.
Both sides will have to defend better against PSG, with Leipzig's woes evidenced as Ake towered over two opponents to head in Grealish's corner before Mukiele inexplicably nodded Kevin De Bruyne's awkward delivery past his own goalkeeper.
Mukiele soon put his head to better use, directing the ball back across goal for Nkunku to nod beyond Ederson, but back came City before the break, this time aided by Lukas Klostermann, whose elbow blocked Ferran Torres' header and allowed Mahrez to dispatch a thumping spot-kick.
The second half followed a similar pattern, with Leipzig twice working hard to get back into the game and then quickly falling further behind.
Grealish's pinpoint finish after cutting in from the left cancelled out another header from Nkunku, who completed his treble shooting across Ederson from the right side of the area.
Cancelo drove in from 25 yards, however, and then provoked a red card from former City man Angelino – dismally late to a challenge when already booked – with time remaining for a scruffy close-range sixth from Jesus.