But who was United's star man at Carrow Road? Our man at the game gives his player ratings.
Simon Moore: 7. Relatively untroubled for most of the game but caught crosses well, and did well to tip over Zimmerman's header and hold onto Murphy's shot
George Baldock: 7. Seemed fired-up all afternoon and endeared himself to the away fans by barging over Maddison. Defended well and got forward when he could, too
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Chris Basham: 7. Got away with a risky pass across the back four but dealt well with lively Murphy down the Norwich left. A lovely Cryuff turn thrown in, as well
Richard Stearman: 7. Brought the ball out well and was a calm, consistent figure in the first half, and then repelled almost everything from Norwich in the second
Jack O'Connell: 7. Helped set up Wilson's opener by taking down the corner from the Blades right. Headed and kicked everything away in the second period
Enda Stevens: 7. Linked up well with Fleck in the first half and helped cut Norwich to bits almost at will at times. A little quieter in the second as Norwich pushed on
Lee Evans: 8. Excellent. Got on the ball at will and kept United ticking over. A very accomplished debut
John Fleck: 8. United's star man. Almost everything that was good about United went through Fleck and he and Stevens cut Norwich apart in the first half
Ryan Leonard: 7. A tidy debut for the long-term United target, who was unlucky not to get on the scoresheet as he was denied by two excellent saves from Gunn
James Wilson: 8. A tidy, promising debut for the on-loan Manchester United man, who linked play brilliantly and took his first Blades goal very well
Leon Clarke: 7. Captained United again and put in a typical workmanlike performance, even if he couldn't get his name on the scoresheet
Subs - John Lundstram: 7. Came on to help United preserve their lead and his willingness to run in behind almost created a chance for a late third
Clayton Donaldson: 8. Perhaps a little unfortunate not to start the game, but came on and put himself about before that industry led to a simple goal after forcing a defensive mistake.
Not used: Sharp, Duffy, Lafferty, Holmes, Eastwood.
Norwich: Gunn 7, Pinto 6, Klose 7, Zimmerman 6, Hanley 6 (Hoolahan 59, 6), Lewis 6, Reed 6 (Vrancic 59, 6), Tettey 6 (Stiepermann 87), Maddison 7, Oliveira 6, Murphy 6. Not used: Husband, Raggett, McGovern, Cantwell.
Referee: Tony Harrington - 6.
Attendance: 26,486