The home side were the better team throughout and they forced Petr Cech into making a couple of decent saves in the first half, from Jack Rodwell and Matija Nastasic, as Chelsea struggled to contain the Toure led City attack.
It was the away side though who had a great chance to take the lead in the second half, when Demba Ba was brought down by Joe Hart in the area and Frank Lampard had the chance to score his 200th goal for Chelsea from the spot.
Hart redeemed himself though as he brilliantly dived to his right to save Lampard's low and hard penalty in a critical moment of the match, which was further emphasised just ten minutes later.
In the 63rd minute, David Silva found Yaya Toure just outside the area and the Ivorian superbly powered his way into the area before bending a right footed shot past Cech to give the home side a deserved lead.
City then looked dangerous on the break through Sergio Aguero and substitute Tevez, who clinched all three points when he collected Silva's pass and smacked the ball past the helpless Cech from 20 yards.