The Blades, without an away win all season, were 2-0 to the good at half-time as two goals in six minutes had Chris Wilder’s men in command.
Cameron Archer fired the visitors in front on the half-hour and six minutes later the lead was doubled when James McAtee converted from the spot after the officials had spotted a handball from Reece Burke.
The Town had a lifeline seven minutes after the restart when Carlton Morris converted a penalty following another handball to half the deficit.
But despite pushing for an equaliser the Blades restored their two-goal cushion when Vini Souza finished well past Thomas Kaminski.
Two goals behind, the Town rallied but couldn’t find a way through a determined defence and the points were heading up the M1.
Town: Kaminski; Ogbene, Doughty (sub Berry 87), Burke (sub Townsend 68), Osho, Bell; Lokonga, Barkley; Clark (sub Chong 53), Morris (sub Woodrow 87), Adebayo.
Subs not used: Krul, Berry, Woodrow, Kaboré, Chong, Mengi, Mpanzu, Brown, Townsend.
Referee: Christopher Kavanagh
Attendance: 11,138, including 1,350 from Sheffield United.