The Canaries struggled in the first half but improved after the break to take the three points.
Norwich boss Paul Lambert paid tribute to match-winner Andrew Crofts whose brace sealed the win.
The former Brighton midfielder now has six goals to his name this season and a delighted Lambert said: "He's created a niche for himself. I think he's one of the best midfielders in the league.
"His all-round game is top-class. I could be biased and every manager will have their own perception of each individual, but in my view he is becoming a really, really top footballer."
Lambert added: "Most of the lads are untried at this level, but my God they are taking to it brilliantly.
"You look at the lads I've taken, they've got great hunger and they deserve every bit of credit that comes their way.
"It's incredible what we have done from where we have come from. In the second half we were excellent."
Blades boss Micky Adams, who is still searching for a first win at his hometown club, fumed that both Norwich goals were the result of infringements.
"With the first one, leading up to the corner, there's quite clearly a trip on Kyle Bartley which the referee missed," he explained.
"It goes out for a corner and the ball then comes in to the box and there is a foul on (goalkeeper Steve) Simonsen in our view.
"Then the second goal, Ched Evans clears the ball and their fella jumps into him. It's a foul, but he (Haines) has missed it again.
"When you are down at the bottom it goes against you, but you hope over the course of a season it evens itself out."
Relegation-threatened United were much the better side prior to the interval, but paid the price for failing to convert their chances.
When asked if the Blades deserved something from the game, he responded: "I thought so, but then I'm going to say that.
"It's a cruel game and I thought that for long periods we dominated and just couldn't get the ball in the back of the net.
"We needed a goal in the first half, but having said that I thought it was the best we've played since I've been here.
"We've played a top-five side today and, at times, made them look average, so I think that's got to be encouraging for us.
"We've got to stick together. What we need now is strong leadership and the players will certainly get that from me."