Rovers suffered a third consecutive defeat to end 2018 in disappointment following three second half goals in the space of eight minutes at Bramall Lane.
Tony Mowbray made seven changes to his team to take on the Blades from the starting XI that began at Leeds United on Boxing Day.
After a goalless first 45 minutes, the drama began just after the break when Chris Basham was shown a second yellow card.
Richie Smallwood was then shown a straight red soon after before Billy Sharp did what he did in the reverse fixture at Ewood Park - score a quickfire brace - to put the Blades ahead.
Strike partner David McGoldrick added a third late on as United ran out comfortable winners and leave Rovers stunned in the steel city.
Harrison Reed, Smallwood, Joe Rothwell, Ben Brereton, Lewis Travis, Elliott Bennett and Kasey Palmer all come into the team, as Mowbray rotated his side during a busy festive period.
The likes of Jack Rodwell, Adam Armstrong, Bradley Dack, Danny Graham and Corry Evans all dropped to the bench, whilst Amari'i Bell missed out on the squad altogether.
The hosts named an unchanged team that defeated Derby County on Boxing Day, meaning Sharp once again partnered McGoldrick up front.
Rovers settled well in the steel city, and the first notable opportunity inside the opening 20 minutes came when Mark Duffy volleyed a couple of yards past David Raya's left-hand post.
At the other end, Charlie Mulgrew's left footed free kick deflected just past the post before centre half partner Darragh Lenihan fired well wide from the resulting corner kick.
A moment later and another Mulgrew free kick cracked against the base of the post before the ball got wedged under the feet of Travis and the danger was eventually cleared.
Midway through the half and the Blades rattled the upright through the rampaging Enda Stevens after John Fleck picked out the Republic of Ireland international.
Stevens again tested Raya on the half hour mark, but a slight deflection took the sting out of the former Portsmouth defender's drive.
United continued to probe and Sharp tested Raya from an acute angle after sneaking in behind the backline, but the Spaniard stuck out a big paw to put the ball out for a corner.
On the stroke of half time, Raya again was called into action; this time grabbing another dipping volley from the experienced Duffy.
Rovers went into the break good value for the 0-0, and could count themselves unfortunate to not have a lead going into half time.
Seven minutes after the break and the hosts were reduced to 10 men when Basham was shown a second yellow card for a deliberate hand ball from another Mulgrew free kick after John Egan hauled down Brereton outside the box.
Rovers were starting to control the game, and on the hour mark it was Williams who tested Dean Henderson down low to his left after Palmer picked out the left back.
The teams were evened up with 20 minutes remaining when Smallwood, on his 28th birthday, picked up a straight red card for taking down Sharp in the home half, with Anthony Taylor handing the number six an early bath.
And two minutes later it was Sharp who handed the home side the lead as he lashed home from close range after latching onto a McGoldrick knockdown.
Four minutes later and it was that man Sharp again who made it 2-0, as he volleyed home from inside the box after a long punt forward found the diminutive frontman, who found the net for the 15th time this season.
Two became three with nine minutes to go when Fleck smashed across goal and McGoldrick chested home from close range as United added gloss to the scoreline against a downbeat Rovers.
There was still time for substitute Leon Clarke to go close to adding to the scoreline, but the experienced striker could only head a dangerous corner over the upright with two minutes remaining.
That meant a disappointing end to 2018 for Rovers, which, in the main, had been a terrific year.
Rovers: Raya, Bennett, Lenihan, Mulgrew (c), Williams, Reed, Smallwood, Travis, Rothwell, Palmer (Armstrong, 69), Brereton (Dack, 69)
Substitutes: Leutwiler, Rodwell, Graham, Downing, Evans.
Booked: Palmer, 58
Sent off: Smallwood, 70
Sheffield United: Henderson, Baldock, Stevens, Fleck O'Connell, Basham, Sharp (c) (Washington, 87), Egan, Norwood, McGoldrick (Clarke, 87), Duffy (Coutts, 56).
Substitutes: Moore, Clarke, Stearman, Johnson, Cranie, Washington.
Goal: Sharp, 73, 77, McGoldrick, 81
Booked: Basham, 9, 52, Norwood, 33, Egan, 50, Sharp, 70
Sent off: Basham, 52
Referee: Anthony Taylor.