Jack O'Connell and Kieron Freeman were the scorers at Bramall Lane as the Blades moved seven points clear of second-placed Bolton and another step closer to the Championship.
Millwall, who saw their 16-match unbeaten league run come to an end with defeat to Swindon at the weekend, remain three points adrift of sixth-placed Southend after seeing their winless run stretch to four games.
The good news for Millwall was that eighth-placed Rochdale failed to capitalise as they crashed to a 3-1 defeat at AFC Wimbledon.
Rochdale were reduced to 10 men on the stroke of half-time when Keith Keane was handed his marching orders and the hosts took full advantage, netting three times in five second-half minutes through Sean Kelly, Lyle Taylor and a Dean Parrett penalty.
Dale pulled a goal back through Callum Camps in the 65th minute but they could not make any further inroads.
Conor McAleny scored a hat-trick as Oxford warmed up for Sunday's Checkatrade Trophy final against Coventry with a 5-1 mauling of Bury.
Marvin Johnson and Joe Rothwell put Oxford in charge before on-loan Everton striker McAleny sealed the points as the U's moved to within four points of the top six. James Vaughan scored Bury's reply but his side were already 4-0 down at the time.
In the only match in League Two, in-form Accrington Stanley moved further clear of trouble with a 2-0 home win over Cambridge, Sean McConville and Shay McCartan the men on the scoresheet.