Nevertheless, the loss yesterday of their unbeaten home record to a resurgent Norwich City, who have now won three consecutive games, provided a reminder to Neil Warnock and his team that there is still some way to go before automatic promotion to the Premiership is assured.
Despite taking a first-half lead, the South Yorkshire side were eventually well beaten after contriving to concede two second-half goals courtesy of defensive errors.
Dean Ashton took advantage for the first of them, after springing United's offside trap, while David Unsworth's own goal was nothing short of farcical.
With 19 minutes remaining Darren Huckerby broke down the left and beat the onrushing Paddy Kenny to the ball, with the goalkeeper left stranded. Huckerby squared to Ashton whose shot was weak and at least two yards wide.
However, Unsworth and Chris Morgan were both on the line and when the latter missed his header, the former, standing directly behind him, could only deflect it into the net. There was not a Norwich player within 15 yards of them - not that the jubilant and disbelieving away fans behind the goal cared.
"It was a Boxing Day Christmas present," said Warnock, the United manager. "I think you could say it was a lack of concentration - that would be one way of putting it. We shot ourselves in the foot today. Our contribution for all three goals was very poor."
Alan Quinn's corner led to the opening goal, Phil Jagielka meeting it with a near-post header. Norwich drew level when Carl Robinson's header found Paul McVeigh, whose precise, angled shot from inside the area rolled into the far corner.
His peculiar and prolonged posturing in front of the home crowd earned him a booking and it might have been worse as a couple of objects thrown from the stand did not find their intended target.
With Norwich persevering with a refreshing three-man front line, the game was both even and fast-paced until Ashton struck with his 11th goal of the season. Adam Drury's long pass looked little more than a clearance but with the United defence appealing for an offside flag that was never raised, the £3m striker had time to steady himself before rifling a low drive beyond Paddy Kenny.
Then came Unsworth's own goal and Norwich are now in the top half of the table, just five points away from Stoke in the last of the play-off spots.
"It was a very, very good result, especially after going a goal down," said Nigel Worthington, the Norwich manager. "In the end I think we were worthy winners and deserved a bit of luck with the third goal. We had a good result last week and this makes it two good results on the spin so we've got to keep that going."
Goals: Jagielka (22) 1-0; McVeigh (33) 1-1; Ashton (62) 1-2; Unsworth og (71) 1-3.
Sheffield United (4-4-2): Kenny; Kozluk, Bromby, Morgan, Unsworth; Quinn, Montgomery (Gillespie, 66), Jagielka, Tonge (Ifill, 72); Shipperley (Kabba, 72), Webber. Substitutes not used: Ifill, Kabba, Armstrong, Geary.
Norwich City (4-3-3): Green; Colin, Doherty, Fleming, Drury; Charlton, Safri, Robinson; Ashton (Thorne, 90), McVeigh (McKenzie, 75), Huckerby (Henderson, 87). Substitutes not used: Ward (gk), Jarvis.
Referee: T Kettle (Berkshire).
Booked: Sheffield United: Quinn, Bromby. Norwich City: Safri, McVeigh, Charlton, Huckerby, McKenzie.
Man of the match: Ashton.