Scott Rendell's 80th-minute goal proved decisive in a clash between teams separated by 85 places on the English football ladder.
The Blue Square Premier side's victory at Carrow Road made them the first non-league team to beat top-flight opposition since Sutton United saw off Coventry in 1989.
The hosts spurned several chances before JJ O'Donnell's cross found Rendell and he slid the ball into the net. Norwich were not the only top-flight team embarrassed, as League One MK Dons won 4-2 at QPR. Armand Traore's fourth-minute own goal and Ryan Lowe's 40th-minute effort had the visitors in control at half-time.
Ryan Harley (50) and Darren Potter (56) made it 4-0 before Jay Bothroyd and Fabio netted for Harry Redknapp's men.
Manchester City booked their place in today's fifth-round draw with a 1-0 victory away to Stoke City. Pablo Zabaleta scored five minutes from time, but victory came at a cost for Roberto Mancini's men as captain Vincent Kompany limped off with a calf strain that will rule him out of Tuesday's trip to QPR on league business.
Manchester United were easy 4-1 conquerors of Fulham in the evening match. Ryan Giggs converted a third-minute penalty before Wayne Rooney (50) and a double from Javier Hernandez (52 and 66) added to the lead. Aaron Hughes, whose handball gave away the early spot-kick, replied for Fulham 13 minutes from time.
Olivier Giroud scored a double for a second consecutive match as Arsenal won 3-2 at Brighton. The Frenchman's goals were both can-celled out, but Theo Walcott scored the winner five minutes from time.
Johnny Heitinga's 90th-minute goal earned Everton a 2-1 success at Bolton. Steven Pienaar's scrappy 18th-minute effort gave David Moyes' men the lead, but Marvin Sordell equalised nine minutes later.
Reading eased into the last 16 with a 4-0 win over Sheffield United with Noel Hunt (six and 50), Mikele Leigertwood (40) and Garath McCleary (54) on target.
Jordi Gomez's seventh-minute penalty gave Wigan a 1-0 win at Macclesfield.
Danny Hylton's 89th-minute goal appeared to have earned Aldershot a replay against Middlesbrough but Lukas Jutkiewicz added to his 83rd-minute effort with a last-minute winner for the Championship side.
Blackburn won 3-0 at Derby thanks to goals from Colin Kazim-Richards (45), Scott Dann (66) and Jordan Rhodes (71).
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