Manchester City's Phil Foden, center, scores during the Premier League soccer match between Burnley and Manchester City in Manchester, England. AP
Esteve turned into his own net under pressure from Phil Foden after Jeremy Doku's effort was saved.
Against the run of play, Burnley hit back through Jadon Anthony to level before half-time.
City were growing frustrated until Matheus Nunes blasted in from Erling Haaland's knockdown.
The unfortunate Esteve turned in Nunes' cross to make it 3-1.
Haaland then struck twice in added time to take his tally for the season to 15 goals in nine games for club and country.
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