Jordi Osei-Tutu, pictured top, scored the only goal, set up by Josh Da Silva, at City's Football Academy just two days after the full-back signed a new contract with the Gunners.
But despite back-to-back wins Arsenal remain eight points off top spot after Liverpool won 4-1 at Sunderland on Sunday. Man City stay eighth.
See: Man City report
Man City: 18 Dec v Chelsea (A), PL2
Arsenal: 15 Dec v Derby (H), PL2