Phil Foden and Riyad Mahrez scored twice apiece and David Silva added to the away side's misery as Burnley's unbeaten run in the top flight came to an abrupt end.
Foden beat Nick Pope from the edge of the box at the midway point in the first half before his Algerian netted twice before the break.
Mahrez collected Fernandinho's raking pass before turning Charlie Taylor inside out and firing into the far corner.
He then beat Pope from the spot minutes later after Clarets skipper Ben Mee had caught Sergio Aguero inside the box.
Burnley's defence was then pulled apart twice in the second half as Silva extended City's lead from close range, converting Bernardo Silva's centre.
And then Foden beat Pope at his near post with his left foot as the ball found its way to the far side of the box.
1. Nick Pope 6
Left exposed by his defence far too often at the Etihad Stadium. However, the England stopper may well feel that he could have done better to keep out some of City's finishes.
2. Matt Lowton 5
Started well and limited City's attacks down his side of the pitch. However, found it difficult to keep the door locked once the home side hit their stride. The full back was out of position in the lead up to the home side's third and fifth goals.
3. Charlie Taylor 5
Given the runaround at times in Burnley's return to action. Recovered well on occasions, but culpable for Riyad Mahrez's first goal of the evening and caught on his heels in the build up to both of City's second half strikes.
4. James Tarkowski 6
Continues to show that he belongs at the highest level of football. Solid first half performance, very rarely putting a foot wrong, though City succeeded in splitting Burnley's two centre backs after the break to add to their tally.