Tyrese Campbell was the architect of the Blades' victory, setting up Callum O'Hare's early opener, then grabbing his fifth goal in six games to make it 2-0 just before the half-hour mark on Tuesday (Wednesday AEDT).
Jesurun Rak-Sakyi rounded out the scoring to complete a dominant display and lift Chris Wilder's men above Yorkshire rivals Leeds, who play Luton on Wednesday (Thursday AEDT).
Scott Parker's Burnley also moved into the automatic-promotion places as they claimed their third straight win at home to managerless Coventry.
Jeremy Sarmiento flicked the opener from the middle of the box two minutes after the interval, and CJ Egan-Riley added a second 10 minutes from time to seal a 2-0 win and leave the Sky Blues still searching for their first win since sacking Mark Robins.
Sunderland lost more ground on their promotion rivals when they played out their fifth straight draw against West Brom at the Stadium of Light.
Chris Rigg and Patrick Roberts both had late chances for the hosts, while the stalemate also extended Albion's frustrating run to just one win from their past 11 matches.
Pressure continues to increase on Hull boss Tim Walter after the Tigers crashed to a 2-0 home defeat against Sheffield Wednesday.
Hull had their chances, with Owls keeper James Beadle saving well to deny Xavier Simons and Regan Slater in the first half.
But a Josh Windass penalty in the 37th minute gave Wednesday the opener, and Michael Smith secured the points with the visitors' second nine minutes from time.
Norwich ended their run of no wins in seven games in spectacular fashion when they thrashed Plymouth 6-1 at Carrow Road.
Borja Sainz grabbed a hat-trick - including two inside the first 17 minutes - while Shane Duffy, Anis Ben Slimane and Ante Crnac also got on the scoresheet.
Mustapha Bundu's 39th-minute effort had briefly reduced the Canaries' two-goal lead, but defeat left Wayne Rooney's men with just one win in eight games.
Ryan Andrews grabbed the only goal as Watford beat Bristol City at Vicarage Road, and Preston had Freddie Woodman sent off in the last minute of a goalless draw at Stoke.
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