Alvaro Negredo, a new signing from Spain, scored three goals while Argentine striker Sergio Aguero added another two to beat the Russians 5-2.
Seydon Doumbia scored both for the Moscow side.
Manchester City now has nine points and will continue on to the knockout stage from Group D along with Bayern Munich, last years winners.
The last meeting between these two sides earlier this year was marred by alleged racism incidents which led City star Yaya Toure to say black players could boycott the 2018 World Cup in Russia.
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