The first period was a better one for Conte's side with good chances for Álvaro Morata and César Azpilicueta, Fernandinho had a good chance for the visitors in the final moments but failed to make a breakthrough.
Pep Guardiola's side picked up the pace in the second period with a decent opportunity for David Silva before De Bruyne broke the deadlock in the 67th minute, Gabriel Jesus had one cleared off the line with five minutes to play but The Cityzens had already done enough to secure a crucial three points.
Soaking up some pressure
City were handed a major blow before their trip to the English capital with star striker Sergio Agüero been confirmed to been out for some time after been involved in a car crash, Conte certainly wanted to get one over a certain a title rival and his side looked to snub their opponent's threat early on.
Their first chance came only three minutes in as N'Golo Kanté got down the right flank before whipping a sweet cross into the area, it found the head of Morata who looked to continue his excellent start to life in a Chelsea shirt but he glanced it over the crossbar.
Thibaut Courtois nearly had egg on his face in the 13th minute when he received a backpass from Antonio Rüdiger, the Belgian was closed down by Gabriel Jesus and the deflection off both their bodies nearly saw the ball go in but was just wide of the mark.
Morata was at it again in the 27th minute as the ball was whipped in looking for the Spaniard but the effort was blocked, it came through to Azpilicueta who fired the ball through the crowd, Ederson getting down well to make a decent save. City broke from that chance through Raheem Sterling, the forward flashed the ball across the face of goal looking for Silva and Jesus but neither could get a touch.
The final chance of the half belonged to The Cityzens as De Bruyne did well to power his corner into the mixer, Fernandinho was there as he put it towards the net but Courtois did well to push the effortaway.
Getting one over his former side
Guardiola's side came out for the second period looking more fired up for the occasion, and had two great chances before they eventually found the crucial goal.
The traveling City contingent will have been left confused how they didn't take the lead in the 66th minute, Kyle Walker played a good ball into Silva whose effort blocked by the defender. The full-back had a second bite of the cherry this time looking for Jesus who jumped the que ahead of Silva, but the ball trickled through untouched.
It didn't matter a minute later as they managed to take the lead, De Bruyne started the move as he played a give-and-go with Jesus and he let rip from the top of the box and Courtois had no chance as the Belgian's effort whizzed into the net.
It could have been secured with five minutes to play as the visitors had an effort cleared off-the-line, Sterling did well to get down the right and his chipped pass found Jesus on the left. The young Brazilian was looking to impress in the absence of Agüero, he did well to get the shot away on the volley only for Rüdiger to head away at the last moment.