It was Pep Guardiola’s 18th win in a row, as City continue to march towards the Premier League title.
City wasted a lot of chances to make the score line more comfortable, after Sterling ran onto Kevin De Bruyne’s pass to open scoring in the first half.
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They now top the table with 58 points, 15 more than city rivals Manchester United.
City’s last league game of the year, will be away to Crystal Palace on Sunday.