City doubled their lead five minutes into a second period and it was Jesus who finished off a move which saw the visitors camped on the edges of the Burnley box for what seemed like a minute.
The set up came once again from De Bruyne picking out Bernardo on the right. His whipped left foot cross hooked in on the volley by the Brazilian.
Jesus could have had a third two minutes later, leaving James Tarkowski toiling but putting his shot on the angle just wide of the far post.
City added a third on 67 minutes and it was a cracker, Rodri capping his best performance in a City shirt with a brilliant hit from outside the box with the outside of his boot.
Robbie Brady pulled one back for Burnley late on – but it was too late as City sent out a message to Liverpool and co..