The Hatters were an 8/1 shot at Ladbrokes before kick-off at Carrow Road but they stunned the Canaries to reach the fifth round.
Oldham meanwhile, at 10/1, saw off Liverpool and Leeds (5/1) defeated Tottenham in a weekend of surprise results.
In the outright betting, Ladbrokes make Manchester United 11/5 favourites to lift the trophy, ahead of neighbours City at 5/2.
Alex Donohue of Ladbrokes told Betrescue: “The spirit of Bradford City is clearly still alive and well in cup football. We’re struggling to remember a weekend with as many shocks as this.”
He added: “Anyone who called all the results this weekend would be able to retire. Thankfully for us not a single punter had their crystal ball out on Friday.”
Ladbrokes latest betting
Shock odds in full
MK Dons win 7/2
Luton win 8/1
Brentford-Chelsea draw 9/2
Leeds win 5/1
Oldham win 10/1
FA Cup winner 2012/13
Manchester United 11/5
Manchester City 5/2