The Canaries took Premier League champions Chelsea all the way to penalties in their FA Cup third-round replay at Stamford Bridge on Wednesday.
Those efforts seemed to have had an impact when James Wilson, on his full debut, put the Blades ahead in the sixth minute, turning the ball home following a corner.
The visitors doubled their lead in the 68th minute when Clayton Donaldson capitalised on an under-hit Alex Tettey pass-back to slot past goalkeeper Angus Gunn.
Norwich rallied and reduced the deficit within two minutes as captain Ivo Pinto headed in James Maddison’s cross but the home side could not muster an equaliser.
Sheffield United manager Chris Wilder praised the efforts of his men to see the match out for three points which keeps them in sixth place.
“It was up to us to get about them. I thought we dominated and dictated the game in the first half,” Wilder said on his club’s website.
“Their goal is a disappointment for us, and all of a sudden it was game on.
“They have some good offensive players at the top of the pitch, so for us to see the game out was great.”
Norwich City: Gunn, Hanley (Hoolahan 59), Zimmermann, Klose, Ivo Pinto, Reed (Vrancic 59), Tettey (Stiepermann 87), Lewis, Maddison, Oliveira, Murphy.
Subs Not Used: Husband, Raggett, McGovern, Cantwell.
Sheffield United: Moore, Basham, Stearman, O’Connell, Baldock, Leonard, Lee Evans (Lundstram 82), Fleck, Stevens, Clarke, Wilson (Donaldson 58). Subs Not Used: Holmes, Sharp, Duffy, Lafferty, Eastwood.
Referee: Tony Harrington (Cleveland).