City had won each of its previous four home games against Burnley 5-0 but this time settled simply for taking three points from a slightly sloppy display.
Coming out of an international break without some key men – and having seen Liverpool thrash Watford earlier in the day – the result was all that mattered.
Bernardo Silva's 12th-minute strike initially hinted at a rather more straightforward affair for the champion, though it was left to Kevin De Bruyne to belatedly make the game safe.
City's two best players from its previous game against leader Liverpool were both involved in the opener, as Silva picked out Phil Foden just inside the box and was then on hand to slam into the net when Nick Pope could only parry the England international's low shot.
However, the home side's unfamiliar back four – missing Ruben Dias and Kyle Walker – afforded opportunities to Burnley, who had Maxwel Cornet shoot too close to Zack Steffen after fine work from Dwight McNeil before Josh Brownhill whipped a low effort wide.
Riyad Mahrez blasted against the crossbar shortly after the break, but frustration built among the home supporters as City again struggled to build on a strong start to the half.
The mood lifted with 20 minutes to play when Ashley Westwood failed to clear and Mahrez toed the ball into the path of De Bruyne for a thumping left-footed finish.
Chris Wood clipped the crossbar from close range when he could have set up a nervy finish, although the forward might have been offside as he met Nathan Collins's knockdown.
City is back in UEFA Champions League action against Club Brugge on Wednesday (AEDT), while Burnley's waits for a first Premier League win of the season takes it to Southampton next Sunday (AEDT).