The Citizens have moved six points clear of the Gunners ahead of the Etihad derby in seven days. On the other hand, the London Blues suffered their third consecutive league defeat and are now four points behind Liverpool, who are in the Champions League zone.
Pep Guardiola's team scored all three goals in the second 45 minutes.
Chelsea's goal was opened by Nico O'Reilly, who headed home in the 51st minute after a cross from Ryan Sharkey.
Just six minutes later, Sherki provided a masterful assist to Mark Guei, who doubled the lead and scored his first Premier League goal in the Citizens' jersey.
Jeremy Douka put an end to the match in the 68th minute.
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