The visitors were off to the perfect start when Edin Dzeko struck inside the first minute.
Samir Nasri pushed through United's napping defence to hit goalkeeper David de Gea's near post. The rebound ricocheted to Dzeko who converted from in close to put City 1-0 ahead.
Dzeko was denied a second after 15 minutes when De Gea saved smartly to his left.
Marouane Fellaini was fortunate to escape with only a booking after a heavy elbow thrown at City fullback Pablo Zabaleta.
Instead, Dzeko put the game beyond United ten minutes after the break.
The Bosnian reacted first to a corner to volley the ball past De Gea. His run left United defender Rio Ferdinand languishing and he connected superbly to divert Samir Nasri's corner inside the post for his 10th league goal of the season.
United huffed and puffed after that second goal, but failed to genuinely test Hart. The England No1 made one smart save from a Danny Welbeck flick, but City were always comfortable.
And they ranout deserved winners as Yaya Toure drove home a third to complete the triumph.
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