Chelsea, Arsenal to meet in League Cup
Javier Hernandez's strike early in the second half secured a 1-0 win at Old Trafford, which will play host to the Canaries the week starting October 28.
Despite their heroics, the Blues are still considered rank outsiders to regain the title they won in 2011, with United amongst the favorites after drawing Norwich.
"Well, you always want a home draw if you can get it,'' manager David Moyes told Sky Sports 1.
"Norwich are a good side, they have got a good manager and we will give them every respect.''
Martin Jol's Fulham travel to Leicester in search of a quarter-final berth in their tie.
The last tie to be decided is arguably the most exciting of the fourth round, with Arsenal hosting Chelsea after Arsene Wenger's side overcame West Brom on penalties on Wednesday night.
Draw in full:
Sunderland vs. Southampton
Leicester vs. Fulham
Birmingham vs. Stoke
Man Utd vs. Norwich
Burnley vs. West Ham
Arsenal vs. Chelsea
Tottenham vs. Hull
Newcastle vs. Man City
Ties to be played on October 29 and 30.