The Whites had dropped to second prior to kickoff at Carrow Road as Middlesbrough ran out 1-0 winners over West Bromwich Albion a day earlier.
However, Marcelo Bielsa's side moved to 13 points, level with Boro but boasting a better goal difference, after Mateusz Klich, Ezgjan Alioski and Pablo Hernandez struck three unanswered goals.
Bolton Wanderers saw their impressive start to the season abruptly halted as they fell to a heavy 3-0 home defeat at the hands of Sheffield United.
Mark Duffy swept home Chris Basham's pass to put the Blades in front after only five minutes, before Kieron Freeman doubled their lead on 22 minutes and John Fleck sealed the points in the second half.
United's win saw them increase their points tally to nine, putting them level with Derby County, Blackburn Rovers and Aston Villa.
Derby and Blackburn both won their weekend games, beating Preston North End and Brentford respectively, while Villa were on the verge of victory only to concede an injury-time goal for a 1-1 draw.
Stoke City picked up a morale-boosting 2-0 home win against Hull City for Gary Rowett's first win in charge, but fellow relegated side Swansea City were beaten 1-0 by Bristol City.
Elsewhere, struggling Queens Park Rangers stopped the rot with a 1-0 win over Wigan Athletic, while Sheffield Wednesday lost 2-1 against Ipswich Town.
Results in full: Aston Villa 1-1 Reading, Blackburn Rovers 1-0 Brentford, Bolton Wanderers 0-3 Sheffield United, Derby County 2-0 Preston North End, Norwich City 0-3 Leeds United, Queens Park Rangers 1-0 Wigan Athletic, Sheffield Wednesday 2-1 Ipswich Town, Stoke City 2-0 Hull City, Swansea City 0-1 Bristol City