They were drawing 0-0 – progress for an injury-ravaged team yet to keep a clean sheet in their one-point start to the season and facing a Wolverhampton Wanderers side who had beaten Manchester City and drawn with Newcastle United and Aston Villa in their last four games.
But that start meant the Blades had to get a win sooner rather than later to ease the pressure on themselves and manager Paul Heckingbottom and a home game against mid-table opposition was not an opportunity they could pass up.
Sir Geoffrey Boycott was in the stands to mark the 50th anniversary of Bramall Lane's last game as a first-class cricket ground before being remodelled for football only.
Had the Yorkshire and England legend given the pre-match team-talk it might have been about playing yourself in on a pitch that was damp to put it mildly at the start before trying to be expansive.
That was the story of a first half where Wolves saw the vast majority of the ball but an excellent defensive display kept them at arm's length, their only chance of note created by a Hwang Hee-chan miskick.
In Premier League terms Auston Trusty was a bargain-bin signing who watched from the sidelines until October but in the first game of November he was far more than a make-do-and-mend solution in a patched-up side, switching from the middle of the back three to its left to help keep Hwang under wraps and ordering team-mates around when the South Korean wandered into areas he did not want to follow him to.
Wolves should have scored when Hwang's slice turned a shot into a pass Rayan Ait-Nouri virtually fell onto to miss an open goal 33 minutes in, but they offered little else.
One reason Wolves saw so much of the ball was that the Blades gave it back so cheaply and so quickly so often. When, in first-half stoppage time, Rhian Brewster's knee succumbed to a problem picked up in training, their prospects bleakened.
So whether it was a good or a bad first half hung on the second. It turned out to be a very good one.
Oliver Norwood revealed the players got together in the week to "clear the air" and reset standards, but judging by the complete change in intent after the break, manager Heckingbottom's half-time team-talk was crucial too.
The crowd responded. Their contribution was big too.
Of 27 players used, only Blades goalkeeper Wes Foderingham's passing was less accurate than McAtee's but playing as one of two inside-forwards as the Blades went from 3-4-1-2 to 3-4-2-1, he provided an outlet to get up the field and his persistent determination more than made up for his off-day.
McAtee lost the ball running down the left in the 73rd minute but closed down Toti Gomes' clearance, the ball bouncing off his shins to Archer, who smashed a brilliant finish in off the crossbar.
Victory looked on the cards until Jean-Ricner Bellegarde swivelled on an 89th-minute equaliser which deflected in off George Baldock. It ought to have destroyed a side low on morale but they refused to let it.
Wolves were unlucky in how the Blades got what they deserved.
When Fabio Silva got what a furious Gary O'Neil described as a graze of his shinpad on Baldock's calf, the makeshift centre-back went down as easily as Hwang and Sasa Kalajdzic did to buy soft first-half free-kicks for Wolves but this was in the penalty area and in stoppage time.
Chris Kavanagh faffed around for an eternity in the video assistant referee’s room but constant replays could not convince him of a clear and obvious Rob Jones error so eventually, the spot kick was given.
Hanging around so long contemplating the enormity of the penalty could have messed with Norwood's mind but he smashed in his shot as emphatically as Archer's.
Suddenly a manager whose job security has been widely discussed recently is only two goals’ difference behind Burnley's Vincent Kompany and two points off Rob Edwards. Theirs – rightly – has not.
It appears the 5-0 defeat at Arsenal which ramped up the pressure played an important part in this win.
"The planning in the Arsenal game was for this as well," said Heckingbottom. "We needed to look after Cam (Archer, on the bench there) and get Rhian minutes and we wanted to stay in a back four against Arsenal because I wanted Gary to be preparing for a back four."
It was all in the groundwork.
Sheffield United: Foderingham; Baldock, Trusty, Robinson; Bogle, Souza, Norwood, Thomas; Hamer (Osborn 90); Brewster (McAtee 45+1), Archer. Unused substitutes: Fleck, Traore, Slimane, Larouci, Osula, Brooks, Amissah.
Wolverhampton Wanderers: Sa; Kilman, Dawson, Gomes (Silva 81); Semedo, Lemina, Doyle (Traore 70), Aït-Nouri; Hwang, Cunha; Kalajdzic (Bellegarde 60). Unused substitutes: Doherty, Bueno, Joao Gomes, Otto, Sarabia, Bentley.
Referee: R Jones (Merseyside).