Daniel Farke's Canaries wrapped up a third successive victory thanks to Teemu Pukki's 15th goal of the season at Carrow Road.
Second-placed Brentford, without injured leading scorer Ivan Toney, suffered a third consecutive loss to dent its bid to reach the Premier League automatically.
Coventry's Tyler Walker scored in each half at St Andrew's, the first from the penalty spot, to move the Sky Blues five points clear of the bottom three.
Swansea City missed the chance to move second after Huddersfield Town returned to form with a 4-1 home win.
Conor Hourihane got the Welsh side back in the game on the stroke of half-time with a brilliant free-kick, cancelling out Fraizer Campbell's opener.
But the Terriers responded in the first 10 minutes of the second half with a Lewis O'Brien goal and Duane Holmes' double securing a first win in nine league games.
Cardiff City and Middlesbrough moved three points off the play-off positions, after Bournemouth lost 2-1 at Queens Park Rangers.
Goals from Stefan Johansen and Todd Kane, either side of Shane Long's equaliser, gave QPR a fourth successive triumph and ended Jonathan Woodgate's unbeaten start as Cherries caretaker boss.
Ashley Fletcher and Marc Bola struck in the first half for Middlesbrough in a 2-0 win at fifth-placed Reading.
Cardiff claimed a fifth consecutive win courtesy of a 4-0 victory over Preston North End.
Nick Powell struck twice and Steven Fletcher was also on target as Stoke City beat Luton Town 3-0.
Managerless Bristol City suffered a seventh consecutive loss in all competitions after Carlton Morris's third goal in as many games gave Barnsley a 1-0 victory at Ashton Gate.
Nottingham Forest condemned Blackburn Rovers to a fourth straight loss with a 1-0 success at The City Ground.
Birmingham City won 1-0 at relegation rival Sheffield Wednesday, while bottom of the table Wycombe Wanderers drew 0-0 with Millwall.