David McGoldrick rounded off the scoring in a game at Bramall Lane that saw both sides reduced to 10 men.
The opening minutes were cagey, with some heavy challenges exchanged. There was a brief stoppage in play as Jack O'Connell had to receive treatment after an aerial clash with Kasey Palmer.
The first shot of note fell to the hosts. Rovers goalkeeper David Raya unconvincingly batted away a corner straight to Mark Duffy just outside the area, who despite bringing the ball onto his right foot saw his volley sail wayward.
Seven changes were made to the Rovers starting XI but they proved themselves credible opponents. From a corner, the ball reached the boot of Darragh Lenihan on the far post, but from a tight angle the centre-half ballooned his effort over the bar.
Not long after Rovers nearly went ahead. Charlie Mulgrew attempted to catch Dean Henderson out at his near post but cursed his luck as the ball smacked the frame of the goal.
United then broke quickly down the right-hand side and swiftly worked the ball to full-back Enda Stevens, bursting into the box from the left flank. From a tight angle, though, his thunderous effort smacked a post and looped out of the danger zone.
United came forward again and Chris Basham threaded a neat ball into Sharp, who was racing into the box. After attempting to take the ball past Raya he forced a good save at point-blank range from the keeper.
Six minutes after the break a spanner was thrown in the works as United were reduced to 10 men. Mulgrew aimed a free-kick goalwards and Basham, in the wall, was adjudged to have handled the ball, earning his second booking of the game.
Despite going a man down the Blades maintained their intensity. Sharp crossed over to McGoldrick but the Irishman was unable to make sufficient contact and saw his header trickle wide of the target.
United still had to be on their guard as Henderson was forced into an excellent save from Derrick Williams. On the break the ball was pulled back to the left-back deep inside the box and Henderson showed good athleticism to get down to his left-hand side to tip the ball wide.
With 20 minutes to go, Blackburn threw away their man advantage as Richie Smallwood received a straight red card for a vicious two-footed challenge on Sharp, giving the referee no choice.
Within minutes United took advantage. In the 73rd minute top-scorer Sharp was sent through on goal and thundered the ball into the net from close range.
Three minutes later Sharp doubled the advantage as, after United cleared the ball from their box, the ball was sent over the top. On the volley, Sharp guided the ball past Raya and into the bottom corner with pinpoint accuracy.
In the 83rd minute the Blades made it three. John Fleck received the ball deep inside the area, and pulled the ball across for McGoldrick, who was able to guide the ball into the net with his chest.
In the dying minutes of the game Blackburn worked to find a consolation, with Lewis Travis getting to the byline, but his pull-back was kicked away by Henderson.