A 100th meeting between the two clubs couldn’t bring a landmark victory for the Clarets as Manchester City extended their perfect home record to return to the top of the Premier League.
Sergio Aguero, Bernardo Silva, Fernandinho, Riyad Mahrez and Leroy Sane got the goals to bring an end to Burnley’s three-match unbeaten run.
But there was controversy about the effort scored by Silva nine minutes into the second half which took the game away from the Clarets and sent the champions on their way to a fifth successive home league win.
Sean Dyche’s men had enjoyed their best spell just before the break and trailed only 1-0 thanks in no small part to the excellence of goalkeeper Joe Hart on his return to the Etihad Stadium.
But their resistance was all but ended when referee Jon Moss – having contributed to confusion over a penalty appeal – allowed Silva’s goal to stand after the ball had gone out of play before the decisive cross.
City duly cashed in as Fernandino quickly added a third, Mahrez curled in the fourth and Sane added a late fifth as Pep Guardiola's side cruised home to take their tally of goals to 18 in five home league games.
But the Clarets will feel events transpired against them on a tough afternoon which also saw City rack up a fifth successive clean sheet to underline their position at the head of English football.
On the plus side, the Clarets were able to include Steven Defour for his first taste of Premier League action since January.
And there was also a warm welcome back for Hart on his return to the club where he made 348 appearances before joining Burnley in the summer.
And the England international was quickly in the action – although not before Sam Vokes had headed a Johann Berg Gudmundsson free-kick over the top at the other end after Vincent Kompany had caught Aaron Lennon high and late to receive a yellow card inside the first 60 seconds.
Hart then made a fine stop to keep out a close-range effort from Aguero, who had already headed wide from a Mahrez cross.
But Aguero can never be kept quiet for long and with 17 minutes gone City’s record goalscorer opened the scoring, sweeping the ball in at the back post from David Silva’s low cross to make it seven goals in seven games against the Clarets.
David Silva then lifted an effort over the top after Charlie Taylor had blocked another shot from Aguero before the Clarets felt their way into the game with their best passage of play.
Burnley enjoyed their share of possession and forced City into mistakes when they over-played at the back.
A fine link-up between Jack Cork and the returning Jeff Hendrick almost produced an equaliser as Hendrick cleverly made space for a shot which was blocked by John Stone.
Gudmundsson curled another effort just wide but City’s goal threat was never too far away and in first-half stoppage time it took a brilliant save from Hart to keep his side in the contest.
This time Bernardo Silva provided the cross for namesake David to meet with a header which brought a flying stop from Hart, who was glad to see Aguero make a rare mess of a chance to pounce on the rebound.
Trailing by only one goal the Clarets were still in the game but a disastrous three-minute spell early in the second half that brought two City goals ended any hopes of snatching an unlikely point.
Burnley didn’t help themselves, but equally were done few favours by the referee, whose indecision spread into the Claret ranks.
After Sane went seemingly untouched to the ground in the penalty area, Moss lifted the whistle to his lips. As Burnley’s players stopped, the official then waved play-on and allowed an off-side David Silva to cross, after the ball had gone marginally out of play, for Bernardo Silva to fire home.
And with Burnley struggling to re-group, they quickly found themselves 3-0 down as Fernandinho rifled the ball into the roof of the net after a corner was cleared to the edge of the penalty area.
City then sent on a fit-again Kevin De Bruyne for his first game since the opening weekend of the season and after Aguero had been denied by the legs of Hart, the Argentinian was replaced by Gabriel Jesus as the champions displayed their embarrassment of riches.
The Clarets made their own double change with just over 20 minutes to go as Chris Wood and Ashley Westwood.
But the contest was effectively over and with 82 minutes gone Mahrez curled home his first City goal at the Etihad Stadium.
There was still time for a fifth goal in the final minute, but again it left something of a bitter taste for the Clarets, who were to suffer their joint biggest margin of defeat in the Premier League.
Sane was fortunate to still be on the pitch after kicking out at Matthew Lowton but having received only a yellow card was able to meet a Benjamin Mendy cross with another clinical finish to equal City's biggest win of the season.
Manchester City: Ederson, Kompany, Stones, Laporte, Mahrez, Fernandinho, David Silva (Foden 74), Mendy, Bernardo Silva (De Bruyne 58), Sane, Aguero (Jesus 66). Substitutes: Muric, Sterling, Otamendi, Zinchenko, Foden.
Booked: Kompany, Sane
Burnley: Hart, Lowton, Tarkowski, Mee, Taylor, Gudmundsson, Defour (Barnes 74), Cork, Lennon (Westwood 69), Hendrick, Vokes (Wood 69). Substitutes: Heaton, Bardsley, Vydra, Long.
Booked: Cork, Hendrick
Referee: Jonathan Moss