Jack Wilshere's maiden Premier League goal at the Emirates Stadium put Arsenal ahead at half-time as he scored his second in successive games, having gone almost three years without scoring in the league.
Norwich threatened on a couple of occasions before Mesut Ozil struck his first Premier League goal for Arsenal just before the hour mark, the Germany international heading home Olivier Giroud's cross.
Jonny Howson's driven finish from the edge of the area after a poor piece of defending from Per Mertesacker gave the Canaries hope.
But any hopes of an unlikely comeback were ended by substitute Aaron Ramsey as he hammered home his ninth goal of the season before Ozil added his second late on.
A late goal from Adam Lallana gave high-flying Southampton a 1-1 draw at Manchester United.
Robin van Persie gave David Moyes' side the lead with his first goal in four games before both he and Wayne Rooney saw efforts hit the crossbar.
But the hosts could not kill off the game and were made to pay as Lallana was on hand to turn Dejan Lovren's shot past David De Gea.
Liverpool were held to a 2-2 draw by 10-man Newcastle in the day's early kick-off at St James' Park.
Yohan Cabaye fired the Magpies ahead with a fantastic long-range effort before Steven Gerrard notched up his 100th Premier League goal from the penalty spot to level the game before half-time.
Mapou Yanga-Mbiwa was sent off for pulling back Luis Suarez for the penalty and it was young defender Paul Dummett, who was introduced to sure up the Newcastle back line, who volleyed home a Cabaye free-kick 11 minutes in to the second half and put the hosts back in front.
Daniel Sturridge again drew Liverpool level in the 72nd minute with a close-range diving header, but Brendan Rodgers had to settle for a point as Newcastle held firm.
Samuel Eto'o opened his Chelsea account as Jose Mourinho's side came from behind to beat Cardiff at Stamford Bridge to win 4-1.
Jordan Mutch had given Cardiff a shock lead on his first Premier League start for the Bluebirds after poor defending from the home side.
David Luiz decided against collecting a pass from Ramires as he looked to leave it for goalkeeper Petr Cech but Mutch nipped in and was left to coolly put the visitors ahead.
It was a mistake from his Cardiff goalkeeper David Marshall that allowed Eden Hazard to equalise for Chelsea.
Marshall looked to bounce the ball and Eto'o nicked it away from him, with Hazard taking full advantage of the Cameroon international's ingenuity.
Eto'o then grabbed his first goal for Chelsea after 66 minutes as he beat two defenders before firing a shot past Marshall.
Mourinho was then sent off after leaving his technical area to vent his upset at a decision, but that did not stop Oscar and Hazard adding the gloss to the scoreline.
Gus Poyet's first game as Sunderland manager ended in a heavy defeat as they slipped to a 4-0 loss at Swansea, the Black Cats remaining anchored to the foot of the table.
The visitors were in the game until two goals in the space of a minute gave Michael Laudrup's side the win.
A Phil Bardsley own goal was followed rapidly by a fantastic strike from Jonathan De Guzman.
The third Swansea goal came courtesy of a Wilfried Bony penalty after Craig Gardner had bundled Leon Britton over inside the box, with Steven Fletcher's own goal making it four with 10 minutes remaining.
Everton had substitute Steven Pienaar to thank for all three points at home to Hull as the midfielder grabbed the winning goal in their 2-1 success.
Kevin Mirallas struck early on to give the hosts the lead at Goodison Park. The Belgium international was picked out from a disputed short corner and his low well-struck effort was unseen by Hull goalkeeper Allan McGregor, going in off the post.
Things went from bad to worse for Steve Bruce's side as striker Danny Graham was stretchered off shortly afterwards.
But it was his replacement Yannick Sagbo who levelled for the visitors as he swept home Sone Aluko's cross from close range.
Hull had a lengthy spell of dominance, but Pienaar marked his return from injury as a second-half substitute by putting the Toffees back in front having been on the pitch for under 30 seconds.
Stoke continued to struggle in front of goal as they drew 0-0 at home to West Brom with Victor Anichebe close to a dramatic late winner for the visitors.
Manchester City moved back in to the top four as Sergio Aguero starred in their 3-1 win at West Ham in Saturday's late kick-off.
The 25-year-old Argentina international slotted the visitors in front after 16 minutes, with gaping holes in the Hammers back four making the finish easier.
He then headed in David Silva's free-kick six minutes after half-time before Ricardo Vaz Te pulled one back with a well-taken strike.
That gave Sam Allardyce's side a glimmer of hope until Silva scored a third 10 minutes from time to give Manuel Pellegrini his first league win away from home.
Head to our Premier League page for reports on all Saturday's matches and reaction from every manager.