The Blades picked up just their second win in 16 league games after beating Port Vale 2-1 at Bramall Lane, with the win also taking Chris Morgan’s side out of the relegation zone.
A 12th-minute Neill Collins header put the Blades in front before Adam Yates scored a fantastic equaliser on the stroke of half-time.
Michael Doyle scored the vital winning goal with a little under 15 minutes remaining to give United’s fans a rare home success.
Bradford City surrendered fourth place to Preston after Phil Parkinson’s side lost 1-0 at Crawley.
The hosts just about shaded the match and took all three points courtesy of Emile Sinclair’s second-half strike.
MK Dons made heavy weather of beating 10-man Rotherham at stadium:mk before eventually running out 3-2 winners.
Michael O’Connor was sent off for Rotherham after conceding a penalty in first-half stoppage time that was tucked away by Shaun Williams.
The result seemed certain when Ben Reeves stabbed home from close range to double the Dons’ lead before Rotherham came right back in to the game.
Lee Frecklington headed home Craig Morgan’s 73rd minute cross with Tom Flanagan’s own goal two minutes later drawing the visitors level.
But Karl Robinson’s side showed great composure to find a winner which came courtesy of an 88th-minute strike from Patrick Bamford.
York had won back-to-back League Tow games but their momentum was ended as they lost 3-0 at Newport.
Chris Zebroski and Lee Minshull struck to put the hosts on course for a win and the game was wrapped up when Danny Crow scored a minute from time.