Gareth Barry, James Milner and Edin Dzeko were also on the scoresheet as the Citizens followed up their victory in St Louis earlier in the week - when they fought back from 3-0 down to win 4-3 - with another thrilling triumph on Saturday evening in New York.
The Light Blues were ahead inside five minutes. Oscar gave the ball away to Sergio Aguero whose strike was blocked by keeper Hilario but only as far as Barry who tapped the ball home from close range.
City got their second on 29 when James Milner fed Nasri who lobbed Hilario before the match at the Yankees Stadium yielded six more goals after the break.
Ramires pulled a goal back for the Dark Blues at the start of the second half after latching on to a long ball from David Luiz.
Shortly afterwards Ramires came close to grabbing a second for Chelsea when his deflected effort was cleared off the line by Milner who netted City's third on 55 after combining with Edin Dzeko.
Ramires grabbed his second of the game on 69 but five minutes later Nasri made it 4-2.
Juan Mata curled the London club's third on 84 before Dzeko completed the scoring with a long range strike that bounced past substitute Petr Cech in what was Rafael Benitez's final game as Chelsea boss.