Daniel Farke's men beat Cardiff City 2-0 at Carrow Road thanks to goals from Emi Buendia and Todd Cantwell, for a fifth consecutive win.
The Canaries pulled further clear of second-placed Bournemouth, which could only draw 0-0 at Luton Town.
"I can't hide the fact I am pretty pleased with our form," Farke, whose side was relegated from the Premier League last season alongside Bournemouth, said.
"We are pleased with our points so far and our position in the league but there is a long way to go. This is the toughest league in the world and we just have to maintain the standards we have shown so far."
Swansea City moved up to third after a 2-0 win over Barnsley.
The Swans made the perfect start on a poor pitch, with Jamal Lowe side-footing home in the second minute.
They doubled their lead in the 66th minute when Barnsley substitute Victor Adeboyejo nodded a Matt Grimes corner past his own goalkeeper.
Brentford is fourth after two superb strikes from Bryan Mbeumo helped it to a 3-1 win against Reading.
Aitor Karanka suffered a heavy defeat against his former club as Birmingham City was beaten 4-1 by Middlesbrough, which moved into the play-off places.
The Blues took a 15th-minute lead but Britt Assombalonga equalised for Middlesbrough and further goals from George Saville, an own goal from goalkeeper Neil Etheridge and a strike by Lewis Wing sealed a comprehensive victory.
Huddersfield Town claimed a 2-0 win against Watford, with a goal from Fraizer Campbell and an own goal from Etienne Capoue.
Sheffield Wednesday beat Coventry City 1-0 while Stoke City saw off Blackburn Rovers by the same scoreline.
Bottom side Wycombe Wanderers scored a late equaliser to earn a point in a 1-1 draw with Queens Park Rangers and Millwall and Nottingham Forest also played out a 1-1 draw.
Rotherham's clash with Derby was postponed after a positive COVID-19 test for a member of Paul Warne's United squad.
The match, which had been due to take place at New York Stadium, was called off less than 90 minutes before the scheduled kick-off time.
An English Football League statement read: "The circumstances surrounding the postponement will now be the subject of an investigation in accordance with EFL regulations.
"A revised date for the rearranged fixture will be confirmed in due course."