Roberto Mancini's side secured all three points despite making the match a lot tougher for themselves than it needed to be, with Samir Nasri receiving a straight red card
City raced into a two-goal lead thanks to two Edin Dzeko goals, but Anthony Pilkington pulled one back before Sergio Aguero got the Premier League champions' third before half-time.
Samir Nasri received a straight red card and Russell Martin another back for the hosts, and later got a second of his own after Mark Bunn had put the ball into his own goal as City claimed all three points.
Despite losing to Chelsea last time out, Norwich only made one change, which saw the much-maligned Steve Morison start in place of Grant Holt, who picked up a late injury.
Roberto Mancini, however, was understandably annoyed with his side's performance against Sunderland with four players suffering in particular. Kolo Toure, James Milner, Javi Garcia and Carlos Tevez all dropped to the bench as Gael Clichy, Gareth Barry, Nasri and Dzeko replaced them.
Last season, Norwich lost 5-1 and 6-1 at the hands of Mancini's side and from the first five minutes it looked like being a similar scoreline. In just the second minute Sergio Aguero and Dzeko combined well down the right before floating the ball over to the left for David Silva, who in turn cushioned it into the area and the Bosnian fired it past Bunn for the opener.
Norwich looked stunned and found themselves even further behind on the visitors' very next attack. Vincent Kompany powered through the middle, riding a challenge from Bradley Johnson before picking out Aguero, who took his time and picked out Dzeko to double his tally.
After the champions' impressive start, the match threatened to calm down, but Norwich had other ideas. Robert Snodgrass' mazy run resulted in a controversial free kick on the edge of the area, and thanks to a deflection from the wall, Pilkington's low effort beat Joe Hart.
Despite the Norwich goal, the champions continued to dominate and almost got a third through Yaya Toure before things turned sour right at the end of the first period as Nasri reacted angrily to a strong challenge from Sebastien Bassong and received a straight red card.
The second period saw the visitors soon grab their third of the day thanks to Aguero. Toure played a great pass over the Norwich defence, but Bassong failed to deal with it and the Argentine forward delightfully lofted it over Bunn and into the net.
It did not take long for Norwich to hit back, however, and they did so through a well-worked corner. After the kick was taken short, Snodgrass produced an excellent cross that Bassong headed back across goal and Martin put it into the top corner.
In keeping with the match, City soon restored the two-goal cushion. Another long ball was played over the Norwich defence and after bringing it down with his chest, Dzeko fired the ball on to the post, but it bounced back on to Bunn and crept over the line.
As the match went on, the scoring continued as Norwich grabbed a third with just over 15 minutes to go. Hart failed to collect a Norwich corner and after an ensuing melee, Martin knocked the ball in for his second goal of the match.
Both sides pressed in the final minutes as Aguero had two very good efforts saved by Bunn, but the champions managed to hold on for the three points.