Sheffield United captain Billy Sharp scored his second goal of the season for the Blades
Norwich are still searching for their first Championship win of the season after an injury-time winner from Billy Sharp gave Sheffield United all three points at Bramall Lane.
Chris Wilder's side took the lead inside the first 10 minutes when John Egan's back-post header looped over Tim Krul.
Jordan Rhodes' second in as many games drew the Canaries level, the Sheffield Wednesday loanee converting Onel Hernandez's cross from close range.
Daniel Farke's men almost clinched victory during a frantic second-half spell - Rhodes nodded a header against the post, Teemu Pukki chipped over from four yards and Mo Leitner was denied in a one-on-one with Dean Henderson - but Sharp's tap-in gave the Blades their second league victory of the season.
The hosts dominated the opening stages, but the first half grew scrappier and United missed a chance to restore their lead after Krul denied Leon Clarke from point-blank range.
The second half was an end-to-end contest - none of the past 17 league meetings between these two sides has ended in a draw - and the Blades repeatedly threatened from set-pieces as Egan and Ryan Leonard inched efforts over.
The visitors looked set to clinch a point as they weathered a late United storm, crowding out Clarke at the back post after Sharp's pass caught Krul out of position, but they could not prevent United's captain netting his second of the season.
That means Sheffield United have still not lost three consecutive home league matches under boss Wilder - they tasted defeat against Swansea on the opening day of this campaign and lost to Preston in their final home match of last season.
Sheffield United manager Chris Wilder told BBC Radio Sheffield:
"The players have shown exactly what they are all about. I know it's only after four games, but the proof is what they do out on the pitch.
"It's a deserved win against a good side. I would have been disappointed if we had drawn and devastated if we had lost because I thought the boys drove the game forward.
"We got ourselves together, we made positive changes and we went for it. I believe that is a fair result today.
Norwich City manager Daniel Farke told BBC Radio Norfolk:
"We were close to winning the game in several periods of the game. A draw would have been a solid result, so to concede so late is tough to take.
"Our defending in general was not bad today. I think they were two equal teams, so for a neutral supporter I would say it was a really good game.
"My job is to lift the players but it's important to let them feel the pain and disappointment after a loss. We have to win more points, that's for sure."
