Norwich teenager Ched Evans - on loan from Manchester City - scored for the second successive game to sink inconsistent Sheffield United. He struck a fine finish from Darren Huckerby's cross after 10 minutes.
The Blades bounced back, with James Beattie volleying just wide and Keith Gillespie also narrowly off target.
Blades' keeper Paddy Kenny saved well from Huckerby and Matthew Pattison, while Gary Cahill had a goal ruled out for the visitors late on.
Norwich City manager Glenn Roeder:
"The first 45 minutes were as well as we've played since I have been here. We knocked it about well and created a lot of chances - and we would have made it a lot easier for ourselves if we had taken a few more of them."
"I was impressed with the way we stood up to them and the manner in which we kept them out in the closing stages."
"Not so long ago we were adrift at the bottom. But they have won four matches out of five to lift us to where we are now. It's happened very quickly and it goes without saying that I'm absolutely delighted."
Sheffield United's Matthew Kilgallon on their late, disallowed goal:
"It was a major decision by the linesman. We couldn't believe it when the flag went up.
"Decisions like that flatten you. We couldn't see where he was coming from."
Norwich: Marshall, Otsemobor, Shackell, Taylor, Camara, Huckerby, Fotheringham, Smith (Croft 63), Pattison, Cureton, Evans (Dublin 73).
Subs Not Used: Arnold, Spillane, Martin.
Booked: Fotheringham, Pattison.
Goals: Evans 10.
Sheff Utd: Kenny, Bardsley, Kilgallon, Cahill, Naysmith, Carney (Hendrie 88), Montgomery, Tonge, Gillespie, Armstrong (Sharp 68), Beattie.
Subs Not Used: Gerrard, Bromby, Stead.
Booked: Cahill, Hendrie.
Att: 24,493
Ref: Darren Deadman (Cambridgeshire).
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