David Silva showed his skill early on, reaching the byline and beating the Norwich defence. However, his cross failed to find a Manchester City player.
City continued to dominate possession but were unable to find a way through the away defence.
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City extended their lead six minutes later, and again it was Aguero who played a starring role, this time giving the ball to Silva who managed to place his shot under John Ruddy.
Norwich's defence then conceded a third inside 25 minutes as City began to run riot. A City corner was met by Matija Nastasic and his header drifted past Ruddy with the aid of a deflection.
By now Norwich were in damage limitation mode, but that didn't stop the home side from scoring their fourth of the first half. Again Aguero was involved, slipping in Alvaro Negredo who slotted in from close range.
It could have been even worse for the away side before the break, but Yaya Toure shot straight at Ruddy.
Toure did get his goal shortly after the break, however, as he curled a free kick into the top corner.
Aguero did his best to make it six, but placed his shot wide.
The striker was not to be denied, as he found the net for his 11th of the season and City's sixth of the afternoon with a volley.