Edin Dzeko's quick brace put City 2-0 up but Norwich reduced the deficit through Anthony Pilkington's deflected free-kick, before Nasri was shown a red card by referee Mike Jones on 44 minutes for putting his head into the face of Sebastien Bassong.
Sergio Aguero's neat flick made it 3-1 at the start of the second half, before Russell Martin's header reduced the deficit again. Dzeko's shot cannoned off the post and in off goalkeeper Mark Bunn to put the Blues 4-2 up, only for Martin's scrambled effort to set up a grandstand finish.
A long ball down the left was worked back inside by Aguero and David Silva for an unmarked Dzeko to sweep home from six yards and the champions swiftly doubled their lead as Aguero was away again, darting into the right side of the Norwich penalty area before drawing the goalkeeper and then cutting the ball back to present Dzeko with another tap-in.
There was some brief respite on 13 minutes when Vincent Kompany tripped Robert Snodgrass just outside the Manchester City penalty area. The Scotland international shaped to take the free-kick himself, but instead ran over the ball, as Pilkington drove in a low shot which deflected off Gael Clichy and past Joe Hart.
Things got ugly just before the break when Bassong upended Nasri on the far touchline. The duo squared up face-to-face, with Nasri pushing his head into the Norwich defender - which on consultation with the assistant referee resulted in a red card for the France midfielder, and a caution for Bassong.
City were soon back on the offensive following the restart and restored their two-goal cushion on 50 minutes. Yaya Toure delivered a perfectly-weighted angled ball which Bassong could not cut out and dropped into the path of Aguero. The Argentina forward produced an exquisite chip to beat the advancing keeper and put City back in control.
To their credit, the home side continued to look to get back into the match, as a low shot from substitute Jonny Howson's was touched wide by Hart. From the resulting short-corner, it was 3-2 when Bassong's header back across the six-yard box from Snodgrass' clever centre was guided into the top right corner by Martin on 63 minutes.
However, City quickly restored their advantage as the broke away down the right. Dzeko sprung the offside trap to burst into the Norwich penalty area to beat Bunn at the near post, the ball bouncing off the woodwork, then the keeper's back and into the net.
A quite amazing match sparked into life once more with 15 minutes left when another Norwich corner caused panic in the City six-yard box as Hart could only half punch clear before Martin swept the ball in again from point-blank range.
Source: PA
Source: PA