Champions Manchester United beat Aston Villa 1-0 to keep in touch with their 'noisy neighbours' and regain the second place they lost earlier in the day to in-form Tottenham Hotspur, 3-0 winners at home to 10-man Bolton Wanderers.
Manchester City have 38 points from 14 matches, with United on 33 and Tottenham 31 but with a game in hand.
Arsenal were the day's other big scorers, thrashing bottom side Wigan Athletic 4-0 to go fifth on goal difference ahead of Newcastle United, 3-0 losers at home to fourth-placed Chelsea.
Argentine striker Aguero opened City's scoring at the Etihad Stadium in the 32nd minute, conjuring a sublime 11th league goal of the season while tightly marked deep inside the penalty area.
Samir Nasri added a second in the 51st and Yaya Toure then scored in the 68th before Steve Morison pulled one back nine minutes from time.
There was no holding off the leaders, with substitute Mario Balotelli coming on and making it 4-1 nonchalantly off his shoulder moments later in the 88th. Adam Johnson then completed the rout in added-time.
"Norwich defended with all their players behind the ball. [Aguero] scored a fantastic goal and the goal Mario scored today was fantastic because it was the only way he could score," City manager Roberto Mancini said.
England international Phil Jones scored his first goal for Manchester United in the 20th minute.
United's win was soured by the loss of Mexican Javier Hernandez to a suspected ankle injury in the 12th minute, while Villa had goalkeeper Shay Given carried off on a stretcher in the 38th with what appeared to be a hamstring problem.
Villa, who replaced Given with Brad Guzan, also lost Jermaine Jenas in the 63rd when the midfielder fell to the ground holding his ankle and without previous contact.
Spurs' sixth straight league win was made easier by Bolton having defender Gary Cahill sent off after 18 minutes - a red card that surprised Tottenham manager Harry Redknapp as much as Owen Coyle in the opposition dugout.
"It was a massive surprise," said Redknapp. "I couldn't see a red card coming, I thought he was going to give Gary a yellow."
There was also a controversy over the absence of a red card at St James' Park, with Chelsea's David Luiz fortunate in the extreme not to be sent off for felling Newcastle's Demba Ba on the edge of the area.
"I asked him [the referee] at half-time why he didn't get sent off, because he was the last man and we were in on goal," Newcastle manager Alan Pardew told Sky Sports television.
"He said to me he didn't have control of the ball. So I'll have to look at the rule book on that one. I'm not exactly sure what he means by that. It's a sending off, simple as that, and it changed the game."
Frank Lampard had a penalty saved but Chelsea still celebrated a m
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