The Canaries took a surprise lead in the 11th minute when Wes Hoolahan's cross was nodded into the area by Leon Barnett and Grant Holt showed great technique to lash home first time.
The advantage lasted just four minutes, with Fernando Torres muscling his way beyond his marker to head Branislav Ivanovic's hanging cross into the far corner.
And with 22 minutes gone, Frank Lampard put Chelsea in front when he met a loose ball at the edge of the area and drilled past John Ruddy.
Eden Hazard made it 3-1 when he stroked home Juan Mata's perfect pass and Ivanovic closed the scoring when he struck a fierce volley with 15 minutes to play.
Defending champions Manchester City recovered some of their swagger as Aleksandar Kolarov, Sergio Aguero and James Milner fired them to a convincing 3-0 win over Sunderland in the day's early kick-off.
The scoreline barely reflected the hosts' dominance as they comfortably recorded their first clean sheet of the season in a one-sided contest at the Etihad Stadium.
There may have been some nerves with only Kolarov's fifth-minute free-kick to show for their first-half efforts, but the Black Cats were then overrun as they slipped to their first loss of the season.
Aguero came off the bench to add the second on the hour and Milner fired a free-kick through Simon Mignolet after 89 minutes.
QPR's winless run extended to seven matches at the Hawthorns, with a 3-2 win for hosts West Brom piling the pressure on Rs boss Mark Hughes.
James Morrison headed the Baggies in front after six minutes and then set up Zoltan Gera for the second after 22 minutes.
The recalled Adel Taarabt put the Rs back in contention when he collected Esteban Granero's pass on his chest before spinning and volleying home, but Youssuf Mulumbu made it 3-1 with five minutes left.
Granero grabbed an injury-time goal but there was no time to rescue a point.
Leighton Baines secured a 2-2 draw for Everton at former club Wigan, scoring an 87th-minute penalty.
Arouna Kone (10) and Nikica Jelavic (11) traded headed goals in a matter of seconds before Franco Di Santo converted Gary Caldwell's cross in the 22nd minute to put the Latics in front.
It looked like that would be enough until Kevin Mirallas earned the spot-kick and Baines stepped up.
Reading gave up a two-goal lead as they drew 2-2 with Swansea at the Liberty Stadium.
Michel Vorm made a rare howler as he allowed Pavel Pogrebnyak's 31st-minute attempt to squirm through him and Noel Hunt's volley doubled the lead moments before half-time.
Michu responded with a diving header in the 71st minute, the Spaniard's sixth goal of the season, and Wayne Routledge levelled seven minutes later as he added the final touch to a wonderful passing move.
In Saturday's late game, Arsenal came from a goal down to beat West Ham 3-1 at Upton Park.
Mohamed Diame opened the scoring in the 21st minute when he netted with a sublime curling effort but four minutes from halftime, the Gunners equalised after summer signing Olivier Giroud poked home his first league goal for the club.
13 minutes from time, Theo Walcott came off the bench to put Arsenal in front, before Santi Cazorla scored six minutes later with a fantastic drive to wrap up the win.
Saturday's Premier League Results
Man City 3-0 Sunderland
Chelsea 4-1 Norwich
Swansea 2-2 Reading
West Brom 3-2 QPR
Wigan 2-2 Everton
West Ham 1-3 Arsenal