City boss Manuel Pellegrini opted to hand the goalkeeping duties to Costel Pantilimon following Joe Hart's error against Chelsea last weekend, but the Romanian had had little to do at the Etihad Stadium as a Bradley Johnson own goal and strikes from David Silva, Matija Nastasic and Alvaro Negredo put the hosts four goals to the good at half-time.
Sergio Aguero, Yaya Toure and Edin Dzeko completed the rout after the break to increase the pressure on Canaries boss Chris Hughton.
Manchester United also enjoyed a comfortable win as they secured a 3-1 triumph over Fulham at Craven Cottage which did little to boost Martin Jol's long-term job prospects.
United led 3-0 inside 23 minutes as Antonio Valencia, Robin van Persie and Wayne Rooney all got on the scoresheet for the defending Premier League champions, before Alex Kacaniklic got a consolation for the hosts.
Asmir Begovic became the fifth goalkeeper to score in the Premier League with a remarkable long-range goal, but it was not enough to give Stoke victory at home to Southampton.
The wind got hold of the Bosnian's long kick downfield and it was allowed to bounce by the Southampton defenders and fly over Saints' goalkeeper Artur Boruc.
But Begovic was beaten by Jay Rodriguez four minutes before the break to make it 1-1, with Saints also having a late penalty appeal for handball against Ryan Shawcross turned away.
Hull boss Steve Bruce enjoyed a win against his former employers as they beat nine-man Sunderland 1-0 at the KC Stadium.
An own goal from Carlos Cuellar was the difference between the teams after the defender headed into his own net under pressure from Yannick Sagbo.
The Black Cats' hopes of a fightback were then dealt a blow when midfielder Lee Cattermole and Andrea Dossena saw red on the stroke of half-time for challenges on Ahmed Elmohamady and David Meyler respectively.
Goals from Saido Berahino and Gareth McAuley gave West Brom a 2-0 lead over bottom side Crystal Palace, while West Ham and Aston Villa played out a goalless draw at Upton Park.
In the day's early kick-off Newcastle had frustrated Chelsea's bid to go top of the table with a 2-0 win thanks to second-half goals from Yoan Gouffran and Loic Remy.