The Canaries made three changes to the side beaten 2-1 at Southampton last time out, with Alexander Tettey, Mario Vrancic and Emiliano Buendia all handed starts.
The visitors gave recalls to strikers Lys Mousset and David McGoldrick, with Billy Sharp and Oliver McBurnie returning to bench duty.
Vrancic and Buendia combined to cause the first threat of the game, with both sides keen to get on the ball and make progress going forward.
Kenny McLean forced Blades keeper Dean Henderson into the first meaningful save of the game and with 25 minutes played it was the hosts who made the breakthrough.
The recalled Tettey met a Buendia corner form the right and, after his initial header fell back to him, he rifled home a left-foot shot which left Henderson totally beaten.
The Blades came under further pressure as both Ben Godfrey and Vrancic threatened for the hosts, with the visitors struggling to pose any real threat up to half-time.
However, United turned the game around within the opening seven minutes of the second half as they stormed into a 2-1 lead.
First Enda Stevens arrived at the far post to head home a deep cross from the right from George Baldock and three minutes later the provider turned goal scorer, finding time and space inside the area to drive his shot past Tim Krul.
The visitors’ hopes of holding on for victory appeared to suffer a blow just over 15 minutes from time when Chris Basham was shown a red card, only for a VAR intervention to downgrade the punishment to a booking.
David McGoldrick then passed up an opportunity to make the game safe as he fired over after being set up by John Lundstram, but it mattered little as the final whistle sounded on a Blades victory.