Charlie Goode was sent off for a rash challenge on Reda Khadra in the second half, while the Rovers man also saw a penalty saved by Wes Foderingham after John Egan handled his cross.
The Blades go within a point of Rovers in the battle for promotion, ahead of this weekend’s trip to Millwall.
Here’s how our man rated the Blades players on an evening to remember at Bramall Lane …
9. John Fleck 6
Plenty of industry and some invention, looking to find the run of Sharp in a combination that has worked so many times before. Photo: Mike Egerton
10. Morgan Gibbs-White 6
A relatively quiet evening, by his own high standards. Struggled to get on the ball and dominate play as he'd have liked, but worked hard for the team when he didn't have it Photo: Mike Egerton
11. Billy Sharp 6
Turned provider with a nice pass over the top to Berge, but he couldn't fashion a shooting chance. Had a great chance from Berge's cross but planted his header wide. Replaced by McBurnie Photo: Mike Egerton
12. Subs: Oli McBurnie 6
Came on for Sharp to give United some aerial presence in both boxes Photo: Simon Bellis