Since Kevin Blackwell was installed as caretaker manager at Bramall Lane, the Blades have taken 27 points from 13 games.
"Eight weeks ago we were four points off relegation so I can't praise the players enough for what they've done," he said.
Incredibly, Blackwell's future is far from secure as his team chase a play-off place. "I'll speak to [chairman] Kevin [McCabe] over the weekend," he said. "We have a meeting that was always arranged and I'm sure we'll have a chat about it. Or maybe he just wants to get on the bus to Southampton."
Saturday's victory was costly, as James Beattie, Ugo Ehiogu and Lee Martin were injured. "If we see those three near a football pitch before the end of the season, it'll be a miracle," Blackwell said. "Two minutes, Beattie gone. 25 minutes and the big centre-half Ugo's gone. Then Martin ruptures his ankle ligaments so at half-time you make a complete change."
At the centre of that "complete change" was the veteran Gary Speed, who headed home the equaliser to a penalty from Michael McIndoe and then scored a penalty of his own, after McIndoe's handball, to win the game.
Two City players – Marvin Elliott and Bradley Orr – have been included in the PFA Championship team of the season. Yet they were not the Robins' players of note on Saturday. Nick Carle ran himself legless on the right flank and Lee Trundle made up for an indifferent season with his best performance.
"There's nobody out there whose ever played in the Premiership," said City's manager, Gary Johnson who is guaranteed a play-off spot, "but we fear no one. Nobody's taken six points off us and we keep ourselves confident. We got up to the winning line almost, but couldn't quite get over it."
Goals: McIndoe pen (25) 0-1; Speed (29) 1-1; Speed pen (55) 2-1.
Sheffield Utd (4-4-2): Kenny; Halls, Kilgallon, Ehiogu (Martin, 25), Naysmith; Cotterill, Speed, Tonge, Quinn; Sharp, Beattie (Hulse, 3), Martin (Geary, 46). Substitutes not used: Stead, Gillespie.
Bristol City (4-4-2): Basso; Orr, McCombe, Carey, McAllister; Noble, Elliott (Showunmi, 76), Carle, McIndoe; Trundle, Adebola. Substitutes not used: Weale (gk), Fontaine, Skuse, Sproule.
Referee: M Halsey (Lancashire). Booked: Sheffield United Cotterrill; Bristol City McAllister.
Man of the match: Speed.
Attendance: 29,787.Reuse content