City's Portuguese international was the first to react in the 12th minute, turning the ball home from close range after Nick Pope had denied Phil Foden at full stretch.
The Clarets fashioned a golden opportunity to equalise when Dwight McNeil released Maxwel Cornet, but the Ivorian was denied with just Zack Steffen to beat.
The visitors missed another gilt-edged opportunity later in the half when Jack Cork interrupted City's plans to play out from the back and, as the ball broke, Josh Brownhill fired just wide of the upright.
Pep Guardiola's side wrapped up the points with 20 minutes remaining when Riyad Mahrez bundled Ashley Westwood off the ball inside the area and De Bruyne finished into the far corner.
Chris Wood could have pulled a goal back late on, when the impressive Nathan Collins helped on McNeil's set-piece, but the New Zealander lifted the ball over the crossbar with the goal at his mercy.
Burnley are now without a win in eight Premier League games this term.
1. Nick Pope 6
Did well to get down to Foden's strike at full stretch, but a tad unfortunate to see the ball fall at the feet of goal-scorer Silva. Saved well to keep out Cancelo's first-time effort, got a fingertip to de Bruyne's looping cross with Stones lurking, and had no chance with the Belgian's finish.
Photo: Oli Scarff
2. Matt Lowton 6
Challenged Foden in the foot race when the young Englishman provided the overlap, largely untroubled by Sterling and fared relatively well overall. However, failed to deliver from wide areas in rare forays forward.
Photo: Oli Scarff
3. Erik Pieters 5
The Dutchman had a tough time coping with City's interchanging flair players. Couldn't contend with Cancelo's pace and trickery, failed to block City's route to goal for the opener and passing generally went astray.
4. Nathan Collins 8
Outstanding. Learning on the job, but what an impression he's made. Built in a similar mould to Tarkowski and Michael Keane. Strong in the air, very rarely beaten with the ball on the deck and made a number of exceptional interventions, including one to stop Foden in his tracks.
Photo: Alex Livesey