Roberto Mancini's side took the lead in the 32nd minute at Eastlands when Argentina forward Sergio Aguero wriggled free of several Norwich defenders before flicking a clever finish into the far corner for his 13th goal of the season.
Samir Nasri got the second when his floated free-kick caught Norwich goalkeeeper John Ruddy flat-footed and crept into the net in the 51st minute.
Yaya Toure scored for the leaders in the 68th minute and, although Wales striker Steve Morison got one back for Norwich in the 81st minute, substitutes Mario Balotelli and Adam Johnson struck late on to ensure City opened up a sizeable gap at the top.
Manchester United, who trail City by eight points, are now under pressure to win at Aston Villa in Saturday's late game.
At St James' Park, Blues manager Villas-Boas was able to silence the critics thanks to goals from Didier Drogba, Salomon Kalou and Daniel Sturridge.
Villas-Boas got an early break as Chelsea were fortunate not to be reduced to 10 men in the fourth minute when David Luiz hauled down Demba Ba.
Referee Mike Dean ruled in Chelsea's favour again in the 14th minute when the official gave a penalty for Yohan Cabaye's trip on Sturridge.
However, Frank Lampard's low spot-kick was weakly struck and Tim Krul pushed it onto a post.
Chelsea took the lead when Drogba struck with a bullet header from Juan Mata's cross in the 38th minute.
Substitute Kalou's 88th minute strike and a cool shot from Sturridge in stoppage time secured Chelsea's second win in their last five matches in all competitions and ended Newcastle's unbeaten home run.
"The referee made a decision that he thought was right not to send off David Luiz, maybe the decision fell our way," Villas-Boas said.
"But it doesn't overshadow the performance of the Chelsea players. It was a win that nobody was expecting."
Tottenham swept into second place with an emphatic 3-0 victory over 10-man Bolton at White Hart Lane.
Gareth Bale prodded Spurs into a seventh minute lead from Luka Modric's corner and moments later referee Stuart Attwell sent off Gary Cahill, harshly ruling the Bolton defender was the last man when he fouled Scott Parker.
Aaron Lennon got Tottenham's second goal in the 50th minute and Jermain Defoe sealed their sixth successive league victory 10 minutes later.
Resurgent Arsenal moved into fifth place with a 4-0 rout of Wigan that pushed the Latics to the bottom of the table.
Spanish midfielder Mikel Arteta opened the floodgates at the DW Stadium in the 28th minute when his long range effort squeezed past Wigan goalkeeper Ali Al Habsi.
Belgian defender Thomas Vermaelen headed the second a minute later, Gervinho netted the third goal in the 61st minute and Robin van Persie made it four in the 78th minute with his 18th goal of the season.
Blackburn striker Ayegbeni Yakubu gave much-criticised boss Steve Kean some breathing space as his four-goal haul inspired a 4-2 win over Swansea at Ewood Park that lifted Rovers off the bottom.
Yakubu opened the scoring in the 20th minute and although Swansea levelled through Leroy Lita in the 35th minute, Yakubu restored Blackburn's lead on the stroke of half-time.
In the 57th minute Yakubu completed his treble before Luke Moore netted for Swansea in the 66th minute.
Swansea's Joe Allen was sent off for a foul on Yakubu, who then stroked home a 82nd-minute penalty.
Heidar Helguson headed QPR into the lead in the 20th minute against West Bromwich Albion, but Shane Long rescued a 1-1 draw with an 81st minute equaliser at Loftus Road.