The visitors opened the scoring in the 24th minute, after Jesus received the ball on the left side and advanced until he entered the penalty area, firing a well-placed shot into the far corner that Bob could not tackle.
In the first half-hour, Burnley was keen to tighten spaces and rely on tight defense, without posing any serious danger to goalkeeper Ederson.
Manchester City have 32 points, temporarily rising to second place, while Burnley have 18 points in 11th place.
Manchester City took a corner in the 6th minute, which De Bruyne deceived in a cross by Angelino on the edge of the penalty area, who had a direct shot completed by Jesus in the net, before the goal was canceled for offside.
City tried to translate his possession into the ball by scoring the first goal, through De Bruyne's break from the middle of the field ended with a powerful ground shot held by goalkeeper Bob.
Manchester City missed an opportunity to score the second goal in the 32nd minute, after De Bruyne sent a distinct cross from the right side, arrived at Sterling who fired but Bob successfully blocked the opportunity.
Manchester City regained their balance by beating Burnley 4-1 in the game at Turf Moor, in the 15th round of the Premier League.
Gabriel Jesus, Rodrigo and Riyadh Mehrez scored in the 24th, 50th, 68th and 87th minutes respectively, while Burnley's Ruby Brady scored in the 89th minute.