Gael Clichy and Sergio Aguero ensured Manchester City claimed a crucial three points despite going down to 10 men in the first half.
Fernandinho saw red for a late challenge on Burnley's Johann Gudmundsson in the 32nd minute.
Pep Guardiola made two changes at half-time by bringing on Aguero and David Silva and the changes worked as City scored two quick-fire goals.
Ben Mee pulled one back after capitalising on a mistake by City goalkeeper Claudio Bravo.
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