Premier League champions in 2012 and 2014, went to the top of the table with a 3-1 victory over West Ham United on Sunday.
They moved on goal difference above Chelsea and neighbours Manchester United, who have also won their three opening games.
Having scored twice in the first 18 minutes through Raheem Sterling and Brazilian Fernandinho, Pep Guardiola's side appeared set for an easy three points, only to be pegged back as the London side improved after halftime.
Michail Antonio reduced the deficit in the 58th minute but Sterling scored his second goal in stoppage time from an acute angle.
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