Dean Henderson earned Sheffield United all three points after a fantastic string of saves in the second half after Billy Sharp put the Blades ahead in the first half.
It was Sheffield United's tenth clean sheet of the season and they were pushed all the way by Norwich City but held on to get the win.
Henderson proves himself once again
After taking the lead through a Billy Sharp header in the first half Sheffield United stayed compact and organised to grind out another victory.
However, it was Manchester United loanee who played a massive part in the victory making a string of jaw-dropping saves.
Most notably he made an outrageous double save from close range to deny Ben Godfrey and then to thwart a sliding Mario Vrancic.
The 22-year-old, who is yet to be capped by the English national side was at his best yet again to deny a firmly hit volley by Jamal Lewis.
Norwich unable to cap off an impressive week
Norwich came into today's game off the back of two victories, one against third-place Leicester City and then beating Tottenham Hotspur on penalties to progress to the quarter-finals of the FA Cup.
Teemu Pukki did come very close to opening the scoring for the canaries after a corner but his effort crashed off the outside of the post.
Despite having more possession and more shots on goal then Sheffield United today Daniel Farke's side just could not find the back of the net.
They remain of the foot of the Premier League table, six points from safety as they host Southampton next weekend.
Billy Sharp scores again
Sharp's first-half header was the only goal today at Bramall Lane and it was supplied by a superb cross by John Lundstram on his return to the starting eleven today.
It was Sharp's third goal in four games and that he only had one for the season but it seems that the United skipper is beginning to pick up some goalscoring form as the home straight of the season begins.
It was an intriguing battle between Sharp and Grant Hanley throughout the 70 minutes that Sharp was on the pitch for but it was the striker that came out on top as he lost the Norwich defenders to head powerfully past Tim Krul to put the Blades 1-0 up.
Sharp will be hoping that he and Sheffield United can carry on their form as they travel to Newcastle next week hoping to avenge their 2-0 defeat to them back in December.