on Saturday afternoon.
The Ivory Coast midfielder raced into the box to provide his side with the decisive goal in the 70th minute, ensuring they kept up with Chelsea and Arsenal, who both won today as well.
Fernandinho had City's first chance in the fifth minute, curling a fine shot towards goal but Potters goalkeeper Asmir Begovic palmed the ball over the crossbar.
It wasn't the most convincing start for the home side though, and Stoke went close next as Charlie Adam's powerful left-footed drive from 20 yards out forced a smart save from Joe Hart.
In the 35th minute, Blues striker Alvaro Negredo made himself half-a-yard of space inside the penalty area after good work from playmaker Samir Nasri, but the Spaniard blazed over the bar from 14 yards.
City's best chance of the half came six minutes before the interval. Yaya Toure received the ball after a one-two with Negredo, but got the finish wrong as he fired his shot high and wide.
City brought on attacking substitutes in Stevan Jovetic and Jesus Navas to help force the issue, and though they spent much of the second half camped in the visitors' half, they failed to create many clear-cut chances.
Jovetic fired a long range effort at Begovic, and though the keeper couldn't hold on to the shot, there was no one following in for City.
City finally broke the deadlock with what could be a crucial goal in this season's title race, as Yaya Toure stabbed home Aleksandar Kolarov's cross from close range with twenty minutes to go.
Manuel Pellegrini's side should have socred again just two minutes later, only for an incredible miss by Dzeko, who appeared to get the ball caught under his foot after Navas played him in for an open goal. The Bosnian then showed his frustration with an angry kick of the goal post.
Ultimately, City did just enough to get past a determined Stoke side, and will welcome the three points however they come after a difficult recent run.
