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 …
5. Jack Robinson 7
His long throw from the left caused problems for Rovers early on, and he showed superb defensive instincts in the second half to put his head where it hurts and nod away before Nyambe could pounce. An assist for the winner too after getting his head to a corner Photo: Simon Bellis
6. Rhys Norrington-Davies 7
Had the ball in the net early on and thought he had given the visitors the lead, but the linesman's flag brought his celebrations to a premature end - much to his disbelief. Had a good running battle with Nyambe, including when he shoved the Rovers man into the advertising hoardings Photo: Simon Bellis
7. Ollie Norwood 6.5
Superb early block prevented Gallagher's shot from surely finding the back of the net. Couldn't assert his usual level of control in midfield but showed some decent moments of passing Photo: Simon Bellis
8. Sander Berge 8
A brilliant deep cross from the right could, and probably should, have brought the first Blades goal but Sharp planted his header wide. Looked so dangerous in the first half as he drove at the Rovers defence. Harshly booked in the second after a clash with Pickering Photo: Mike Egerton