Gareth McAuley\'s own goal put the Red Devils ahead before Robin van Persie scored in injury time. The Red Devils retained their seven-point lead over City.
Old Trafford: Manchester United will head into 2013 with a seven-point cushion atop the Premier League after beating West Bromwich Albion 2-0 on Saturday, although Manchester City kept in touch on Saturday with a gutsy 4-3 win at Norwich.
Gareth McAuley's own goal and a league-high 14th strike of the campaign by Robin van Persie earned United a seventh straight home win and leaves City with a mountain to climb to retain their title.
The champions withstood the first-half dismissal of playmaker Samir Nasri for an apparent headbutt to hold off Norwich, with Edin Dzeko (2) and Sergio Aguero answering manager Roberto Mancini's call for more goals from his strikers.
City were 2-0 ahead after four minutes at Carrow Road thanks to a double from Edin Dzeko, but Anthony Pilkington's free kick halved the deficit before Nasri was dismissed after squaring up to Sebastian Bassong in the 44th minute.
Sergio Aguero restored City's two-goal lead five minutes after halftime, only for Russell Martin to make it 3-2 in the 63rd and then 4-3 in the 75th after Norwich goalkeeper Mark Bunn had deflected in Dzeko's low drive for an own goal.
The champions had some nervy late moments but hung on to stay within touching distance of United heading into 2013.
After starting the game in such dominant fashion, City - surprisingly beaten 1-0 by Sunderland on Wednesday - looked in the mood to cruise to victory, only for the momentum to change because of Nasri's straight red card.
It was a dubious decision by referee Mike Jones, with the France playmaker squaring up to Bassong after being clattered by a robust challenge from the defender. The pair's foreheads clashed - and Nasri motioned a butt - but while Bassong was given a yellow card, the City player saw red.
"I don't know why, as the linesman was there and I don't know what he saw," City manager Roberto Mancini said. "We saw (on) the video both players touch heads."
Mancini will be delighted to see his strike force answer his call for more goals, having criticized them this week for being "soft" in recent games.
Dzeko replaced the ill Carlos Tevez up front to score twice and almost grab a hat trick, with City's fourth credited as an own goal after his shot hit the post, came back out and rebounded off Bunn into the back of the net.
"The guys played very well," Mancini said. "It was like at Sunderland but this time we scored. Today we showed we are there for the title."
Dzeko's first came in the second minute when he sidefooted in coolly from 12 yards and the Bosnia striker made it eight for the season by slotting into an empty net from Aguero's cut-back.
City were left aggrieved when Pilkington's free kick deflected in off Gael Clichy, a double blow since the original foul on Vincent Kompany was harshly awarded.
Down to 10 men for the second half, City needed a quick lift and Aguero provided it, running onto Yaya Toure's fine through-ball in the 50th and scooping a delightful finish over Bunn. Martin scrambled in close range goals either side of Bunn's own goal, but Norwich couldn't find the equalizer.
Tottenham came from behind to beat Sunderland 2-1 and move provisionally third - a point ahead of Chelsea, who visit Everton on Sunday.
Also on Saturday, Wigan moved out of the relegation zone with a 3-0 win at Aston Villa. Ivan Ramis put the visitors ahead in the third minute by heading in a corner from Jean Beausejour, and struggling Villa never recovered.
Emmerson Boyce and Arouna Kone added goals within a four-minute span after the break for Wigan, who climbed above Villa into 16th place in the standings.
Pavel Pogrebnyak's early goal earned Reading a 1-0 victory over West Ham, provisionally lifting his team three points clear of last-place Queens Park Rangers in the standings. The Russia striker latched onto a poor back pass by defender James Collins and planted a low finish into the corner in the fifth minute. Reading goalkeeper Adam Federici produced some fine saves to preserve the lead and ensure the team won only its second game of the campaign. The hosts are still five points adrift of safety in their first season back in the English top flight. Villa are still just above the relegation zone, one point ahead of Southampton.
Swansea capitalized on mistakes by backup goalkeeper David Stockdale to beat struggling Fulham 2-1. Stockdale was making his first top-flight appearance for 11 months in place of the injured Mark Schwarzer and was partly at fault for both goals - by Danny Graham in the 19th minute and Jonathan de Guzman in the 52nd.
Fulham pulled a goal back when Bryan Ruiz's shot went in off an offside Sascha Riether, but still slipped to a defeat which leaves them four points above the drop zone.
The first goal came after Stockdale pushed a cross straight back into danger, and Graham hooked the ball back into the net.
Stockdale then cleared the ball straight against Brede Hangeland and it rebounded for Pablo Hernandez to square for De Guzman to sidefoot home.
Also, Cameron Jerome's 90th-minute volley rescued a point for Stoke in a 3-3 draw with Southampton.
Having just had a goal ruled out for offside, Jerome's long-range shot struck the underside of the bar and crashed into the net, sending the crowd at Brittania Stadium wild. Southampton led 1-0 and 3-1 after strikes from Ricki Lambert, Jay Rodriguez and an own goal by Andy Wilkinson. But Kenwyne Jones and Matthew Upson scored for Stoke to set up Jerome's dramatic late response.
Steven Nzonzi was shown a straight red card in the 71st minute for a challenge on Jack Cork. Stoke stayed in eighth place in the standings with 29 points, while Southampton dropped a place to 18th spot in the relegation zone.