Roberto Di Matteo's unbeaten Chelsea have made a flying start to their title challenge and this was the European champions' sixth win in seven league matches.
The Blues recovered from the shock of Norwich striker Grant Holt's 11th-minute opener at Stamford Bridge to take complete control before half-time.
Fernando Torres equalised with his fifth goal of the season when the Spaniard headed home from a Branislav Ivanovic cross in the 14th-minute.
Frank Lampard put Chelsea in front in the 22nd-minute with a drive from the edge of the area and Belgian playmaker Eden Hazard, netting a cool 31st-minute strike from Juan Mata's pass, shattered Norwich's resistance.
Ivanovic rubbed salt into Norwich's wounds when he bagged the fourth goal with 14 minutes left.
"Norwich scored a good goal and it was important to equalise quickly. From there on it was a lot of Chelsea pressure," Di Matteo said.
"The players just controlled the game. We can be happy about the performance. We are slowly evolving and don't concede too many goals."
Roberto Mancini's City spluttered through the start of their title defence and assault on the Champions League, but a convincing display at Eastlands secured a second victory in their last seven fixtures in all competitions and their first cleansheet of the season at the 10th attempt.
The hosts were ahead after five minutes when Serbian defender Aleksandar Kolarov curled a superb free-kick past Sunderland goalkeeper Simon Mignolet.
Argentine substitute Sergio Aguero got the second goal on the hour when he steered in a Kolarov cross from close-range for his first goal at Eastlands since the dramatic strike that won the title on the final day of last season.
And England midfielder James Milner ensured City would move into second place with an 89th-minute free-kick that glanced in off Sunderland's Craig Gardner.
"In the first half we missed two or three chances like in other games, but we had a good performance," Mancini said.
"Every game is difficult in this moment. I am happy because we got a clean sheet and scored three, but also because of our performance."
Third-placed Everton salvaged a 2-2 draw at Wigan thanks to a late penalty from Leighton Baines.
Wigan went ahead in controversial circumstances when Arouna Kone finished off a fine run from Shaun Maloney even though the Ivory Coast striker was clearly offside.
Everton hit back one minute later through Nikica Jelavic, the Croatia forward heading home for his 13th goal in 16 league starts.
The Latics regained the lead through Franco Di Santo in the 23rd minute, but England left-back Baines fired home from the spot following Maynor Figueroa's foul on Kevin Mirallas with three minutes to go.
West Bromwich Albion continued their surprising start to the season as the Baggies climbed to fourth place with a 3-2 victory over bottom of the table QPR at the Hawthorns.
Steve Clarke's team took the lead after just five minutes when Scotland midfielder James Morrison fired into the bottom corner and the hosts increased their advantage through Zoltan Gera in the 22nd minute.
Morocco midfielder Adel Taarabt gave QPR hope with a fine volley in the 35th minute, but Youssouf Mulumbu clinched the points five minutes from full-time and Esteban Granero's stoppage-time effort was no consolation for the winless visitors.
Reading blew a chance to secure their first league victory of the season as Swansea recovered from two goals down to draw 2-2 at the Liberty Stadium.
The Royals opened the scoring through Russian striker Pavel Pogrebnyak's 31st minute goal and Noel Hunt doubled their lead on the stroke of half-time.
But Michu's 71st-minute goal gave Swansea a lifeline and winger Wayne Routledge levelled seven minutes later. – Sapa-AFP.