Sterling scored from six yards with a shot into the bottom right corner off a cross from Bacary Sagna in the 47th minute.
Fernandinho added a second goal less than 10 minutes later at Etihad Stadium with a firm strike after an assist from David Silva.
City won its 10th straight league match to set a club record. It leads the league with 12 points from four games this season, having scored 10 goals and conceded none.
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