The Canaries capitalised on a slip-up from Sheffield United, who were beaten by Nottingham Forest at the City Ground, while Middlesbrough were held by Stoke City in the late kick-off.
Elsewhere, Paul Gallagher came off the bench and scored before having to play in goal for the closing stages of Preston NorthEnd's 1-1 draw with rock-bottom Ipswich Town.
Meanwhile, Derby County bounced back from its Carabao Cup defeat to Chelsea by ending Birmingham City's 11-match unbeaten streak, and Thomas Frank claimed a first win as Brentford boss.
Brentford finally got their first win under new boss Frank, with Sergi Canos and Ollie Watkins getting its goals in a 2-0 win over Millwall.
Meanwhile, Reading eased the pressure on Paul Clement by coming out on top in a five-goal thriller against Bristol City.