The Blades skipper scored his 16th of the season, and the 219th Football League goal of his career, as Chris Wilder's men continued where they left off on Boxing Day against Derby.
It wasn't all smooth sailing, however, and they were reduced to ten men with the score still goalless when Chris Basham was showed his second yellow card by referee Anthony Taylor.
But Taylor soon redressed the balance by sending off Richie Smallwood for a terrible tackle on Sharp, and the United skipper's double - with a third from David McGoldrick - helped the scoreline appear more routine than it perhaps was.
Earlier, both sides struck the woodwork in a first half that lacked any real sparkle, Rovers captain Charlie Mulgrew rattling the base of Dean Henderson's post from a soft free-kick and Enda Stevens hitting the bar with a powerfully-struck shot following good work from Mark Duffy and John Fleck.
Basham picked up his first caution for a foul on Harrison Reed, many observers believing the challenge to be a fair one, and the handling of Rovers goalkeeper David Raya was tested by Sharp, Duffy and Stevens, with varying degrees of difficulty.
United began the second half as they did the first, on the front foot, but were almost caught out when Ben Brereton was set free on goal. John Egan dragged him back and was booked, and when Mulgrew stepped up and hit the wall with his shot there seemed little danger.
Taylor, though, had spotted a handball by Basham and he was given his marching orders, although replays later suggested the United defender hadn't moved his arm towards the ball.
Smallwood later followed him down the tunnel after a terrible challenge on Sharp, the midfielder exchanging words with Alan Knill as he left the field, but the growing tension around Bramall Lane was lifted when Sharp powered home his first, a patient left-footed finish after linking up with McGoldrick.
His second came moments after a penalty claim by Rovers at the other end, a venemous volley which left Raya with no chance, and McGoldrick applied the gloss to the scoreline when he chested home John Fleck's cross from close range.