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.
Here are the ratings.
9. Ashley Westwood 6
Pressed hard and high, making it as difficult as possible for City to play out from the back, but often left with plenty of ground to cover when the hosts were able to play through it. Brushed off the ball by Mahrez after poor first touch, which allowed De Bruyne to wrap up the points.
10. Jack Cork 6.5
Demonstrated an unwavering desire to get back behind the ball whenever City turned over possession and countered. Showed a little bit of bite when closing the ball down and engineered the chance for Brownhill when foiling City's attempts to play out from the back.
11. Chris Wood 5
Didn't start too badly when holding the ball up and bringing team-mates into play, but couldn't keep it up. Penalty appeals fell on deaf ears when the Kiwi collided with Steffen and he somehow missed the target with the goal at his mercy from Collins' flick. Photo: Jan Kruger
12. Ashley Barnes 5.5
Squandered a golden opportunity to draw Burnley level just seconds after his introduction. The striker tamely shot at Steffen from a promising position after McNeil had charged down a clearance. Contributed little else on the whole. Photo: Oli Scarff