Remarkably, it was the fourth time in a row that a trip to the Etihad had ended in a 5-0 defeat for Sean Dyche’s side.
The Algerian set City on their way in the sixth minute, finishing off a flowing passing move with his trademark cut in from the left and drive into the far corner.
There was a similar finish for the second after Mahrez picked up the ball in space in the area after Burnley had been caught out by a quick throw-in.
Mendy made it 3-0 in the 41st, volleying home at the back post after a fine cross from De Bruyne.
Burnley enjoyed some relief from the pressure after the break with Jay Rodriguez forcing a save out of Ederson with a well-struck effort from a tight angle.
But Ferran Torres then added the fourth goal, slotting home after the overlapping Kyle Walker had found Gabriel Jesus in the box and the Brazilian flicked it to his Spanish teammate to confidently convert.
Mahrez completed his hat-trick in the 69th minute, heading home a Phil Foden cross, and it could have been 6-0 had an effort from Jesus not been ruled out for offside by VAR and a shot from De Bruyne not crashed against the post.