Bernardo Silva struck after 12 minutes to set City on their way to a win over a Burnley side that remain without a Premier League victory this season. Kevin De Bruyne added another in the second half to make the game safe.
Raheem Sterling made a rare start in a week where he said he could look to move away from the club in search of regular playing time, but failed to find the target as Pep Guardiola's men laboured their way to three points.
"After the international break it's always a little bit difficult to come to a rhythm and I know how good Burnley are. They did really well, they have good players," City boss Guardiola said.
"We did well in the second half and played really well and could've scored more goals. Good result, after the international break we take the victory and look what's next."
Burnley's last three trips to City resulted in 5-0 defeats ahead of Saturday's match and they had a familiar sinking feeling early on when they fell behind. Silva was involved in the build-up as he linked up with Joao Cancelo and after Burnley keeper Nick Pope could only spill Phil Foden's shot, Silva thumped in from a yard out.
City were dominant in the early stages but were indebted to United States international Zack Steffen midway through the first half when he raced out to block Maxwel Cornet when he was through on goal. Burnley got even closer 10 minutes before the break when Josh Brownhill dragged an effort inches wide of Steffen's post when he really should have done better.
With 20 minutes remaining, De Bruyne ensured City of the points with an emphatic strike to put the result beyond doubt.
"We get nothing from the game but I was actually pleased with the performance against a top side," Burnley boss Sean Dyche said.
"They created chances, not as many as in the past but I was pleased we were creating quality chances and that's the challenge we've had all season -- taking our chances."