Town were already trailing to two goals inside three minutes from Rhian Brewster and Jack Robinson, when central defender Reece Burke was sent off for pulling Brewster back when he was in on goal with half-an-hour still to play.
Manager Nathan Jones had made two changes to the side that won 2-0 at Reading in midweek, with Admiral Muskwe starting up-front alongside Cameron Jerome following Zimbabwe's exit from the Africa Cup of Nations, in place of Elijah Adebayo who was amongst the subtitutes.
Henri Lansbury came into midfield ahead of Jordan Clark as the gaffer freshened up his side with the Hatters searching for their third win of the week.
The hosts had the game's first attempt on goal, right wing-back Jayden Bogle's 20-yard angled drive comfortable enough for James Shea to deal with, before ex-Hatters loanee Rhys Norrington-Davies' speculative volley deflected off Reece Burke for a corner.
It was the Blades who continued to dominate possession in the opening stages, Rhian Brewster shooting straight at Shea on 16 minutes before the ex-Liverpool youngster fizzed a 25-yarder just past the post a couple of minutes later.
The Hatters strung together their first move of note on the half-hour, when Pelly-Ruddock Mpanzu played a one-two with Allan Campbell on the edge of the Blades' area, then fed Peter Kioso to slide in a cross from the right, but home keeper Wes Foderingham got down low at his near post to keep out Jerome's effort.
Town had the ball in the United net six minutes before half-time, but Sonny Bradley's header from Henri Lansbury's free-kick - after Amari'i Bell had been tripped surging down the left - was ruled out by an offside flag.
The Blades ended the half as they started it, trying to find a way through a Hatters backline that was being organised brilliantly by the captain with Burke and Kal Naismith either side of him, Shea fielding another weak effort from Brewster with two minutes to go until the break.
Three minutes after the restart that changed, when Bogle's wayward cross-shot landed at Brewster's feet in the middle of the Hatters' box, and the 21-year-old managed to lash a right-footed shot past Shea from ten yards out.
Three minutes later it was two, when Robinson was left with the freedom of the Town box to meet Oli Norwood's inswinging free-kick from the left with a firm header past Shea.
Jones wasted no time in introducing Adebayo from the bench, bringing the top scorer on for Jerome in the 53rd minute - although it was Shea who was next to be tested, again by Brewster, whose volley was saved well by the foot of his near post.
By the hour mark the manager had thrown Jordan Clark into the mix in place of Bell, but the afternoon went from bad to worse in the 62nd minute when Burke was shown a straight red card by referee Stephen Martin for dragging Brewster down when he looked to be clear on goal.
Before play restarted, Jones brought Gabe Osho on for Muskwe, but it was Norrington-Davies who was next to have a go, his 64th-minute shot from the edge of the box flying high over the bar, before Norwood did likewise from 30 yards out.
Norrington-Davies was determined to try to get on the scoresheet, but after a far post header was too high, a left-footed half-volley was deflected behind by Osho for a corner and a shot with his weaker right foot was skewed well wide, with Blades skipper Billy Sharp sending an 83rd-minute shot into the side-netting in between.
Town never looked like reducing the deficit, in honesty, with four games in a fortnight appearing to catch up with them after the Covid-enforced winter break and another of those rearranged games against Bristol City to come back at Kenilworth Road on Tuesday night.
Goals:
Sheffield United - Brewster 48, Robinson 51
Att: 27,780
