City dominated much of the game and were rewarded when De Bruyne found the back of the net in the second half to push his side ahead of Manchester United on goal difference at the table's summit.
Chelsea had an early chance after three minutes with N'Golo Kante picking out Alvaro Morata in the middle, only for the striker to head just wide of the target.
City could have had a goal shortly after when Gabriel Jesus charged down a poor Thibaut Courtois clearance, but luckily for Chelsea the ball flew over the bar.
The visitors started to control proceedings and were denied by Courtois on the half-hour mark when the Chelsea keeper got down low to thwart David Silva at his near post.
And the Chelsea No. 1 was called into action again on the stroke of half-time, this time saving Fernandinho's header from close range.
City's dominance continued into the second half and on the 54th minute they could have edged ahead, but Raheem Sterling fired a loose ball on the edge of the box over the bar.
Chelsea managed to create an opening on the hour-mark when a quick free kick found Eden Hazard unmarked in the box, but Ederson was on hand to tip away his effort at goal.
The deadlock was finally broken in the 67th minute through City when De Bruyne received the ball on the edge of the area before firing a fine strike past Courtois and into the back of the net.
City could have killed off the game late on when Gabriel volleyed Sterling's cross goalbound, but Antonio Rudiger was able to clear his effort off the line.