The Belgium international put the treble-chasing visitors ahead after just five minutes when picking out the top corner from Raheem Sterling’s cushioned pass.
City, who briefly dropped to second after Liverpool took care of Watford in the day’s early kick-off, doubled their lead in the 25th minute as Gundogan steered the ball past Nick Pope from another Sterling assist.
Here are the player ratings from Turf Moor.
1. Nick Pope 5
Might have been able to do a little better with Gundogan's finish, but helped keep City's tally down to two. Beat away Rodri's drive in the first half and then produced an almost identical stop to deny Sterling after the break. Photo: Julian Finney
2. Connor Roberts 4
Always going to be up against it when faced with Cancelo and Grealish, and so it proved. Susceptible to balls over the top, struggled to stem the threat at the byline, and distribution was generally disappointing. He did, however, get a toe to a Jesus strike to turn the ball on to the post. Photo: James Gill
3. Charlie Taylor 4.5
Always having to make up ground on Sterling as the England international capitalised on the full back's narrow positioning. Did extremely well to recover on occasions in the first half, but he was overawed in the second half when Sterling, De Bruyne and Walker combined in cutting fashion. Caught ball-watching for the opening goal. Photo: Stu Forster
4. James Tarkowski 5.5
Perhaps guilty of sitting too deep on occasions as City were allowed to collect the ball and get shots away in explicable amounts of space in and around the box. However, the pick of the bunch defensively and helped keep the numbers down. Photo: Nathan Stirk