Two goals from Harry Maguire - getting on the end of Stephen McGinn set-pieces - put the Blades on the road to victory at Bramall Lane.
Ryan Flynn added a third goal before Max Clayton replied for the visitors.
Bradford City let a lead slip as they lost 2-1 at home to Wolverhampton Wanderers.
Raffaele De Vita gave the Bantams in the 15th minute after good work from Kyel Reid.
But goals from James Henry (28) and Richard Steadman (32) earned Wolves victory and saw them climb into second place in the table.
They trail League One leaders Leyton Orient after the London club edged out Rotherham United 1-0, Kevin Lisbie providing the 30th-minute winner.
Goals in either half condemned York City to a 2-0 defeat at home to Fleetwood.
Gareth Evans banged in a 24th minute opener before Jamille Matt doubled the advantage on 67 minutes.