The former Bradford City defender had been in the Baggies side that took a 3-0 lead against the Blades only for the game to be abandoned due to the hosts being down to six men.
There was no repeat last night of those ugly scenes – three red cards were shown to the hosts before Michael Brown and Rob Ullathorne limped out of the action to force that abrupt early curtailment in March, 2002.
Instead, the acquisition of three points by Moore’s men was much more comfortable than the narrow margin of victory suggested.
Goals in each half from Gareth Barry, his first for almost exactly a year, and Kieran Gibbs were enough to condemn the Blades to a third home defeat of the season despite taking a deserved lead early on through David McGoldrick.
His sixth goal came when the hosts were firmly on top, but once pegged back shortly before half-time there was only ever going to be one winner.
No wonder Moore, whose previous three trips to Yorkshire this term as Albion manager had yielded just a point, wore a broad smile at the final whistle after seeing his side leapfrog United into third place.
The Baggies had been far from at their fluent best not least in that opening quarter against Blades in which Tosin Adarabioyo, a 6ft 5ins centre-half had looked hugely vulnerable at right-back.
But such was the disappointing manner in which manager Chris Wilder’s side lost their way after that bright start, Moore’s men had no need to copy their predecessors from 16 years ago by fighting their way to victory at the Lane.
United’s night of contrasts was perhaps best summed up by the two first-half goals.
Their own opener on 12 minutes encapsulated much of what has made Wilder’s Blades such a pleasure to watch for these past two-and-a-half years.
Chris Basham, as likely to pop up in attack on a barnstorming run as fulfilling a central defender’s usual duties, broke up an Albion move deep in home territory on the right touchline.
A simple pass to Oliver Norwood was followed by an equally sensible offload to Mark Duffy.
At 33, the Liverpudlian is invariably the man who makes the Blades tick and his through ball for McGoldrick to chase was delivered with typical pinpoint accuracy.
McGoldrick did the rest by holding off Craig Dawson before drilling a low shot beyond Sam Johnstone.
The flipside to this impressive team goal came when Albion equalised four minutes before the break.
As the home defeat to Leeds showed earlier this month when Pablo Hernandez was gifted the winner, the Blades can make life unnecessarily hard for themselves.
Norwood did just that with a shockingly loose pass deep in his own half. The summer signing, facing his own goal so effectively blind to what was behind him, recklessly tried to spread the play to the right flank.
He managed to find only an Albion shirt. Harvey Barnes, the main reason why Albion were able to rescue a point from a 2-2 draw at Hillsborough on their previous visit to the Steel City in October, then left Basham trailing horribly with a dart down the wing.
His drilled cross then evaded a scrum of red and white shirts, and Barry arrived on cue to fire past Dean Henderson.
Once level the Baggies took full control as Henderson twice pulled off fine saves to deny Phillips and Barnes.
Dwight Gayle and Jay Rodriguez then spurned good openings as the game moved into the final quarter with the visitors looking the far more likely to snatch a winner.
Sure enough Albion struck with 15 minutes remaining and Barnes was once again a central figure with a delightful flick into the path of Gibbs.
He made no mistake from close range to cap a lovely passing move that had seen goalkeeper Johnstone play his part with a delightful chipped pass to the flank that was followed by Matty Phillips leaving John Egan trailing via a searing burst of speed.
Billy Sharp did have a late chance to level, but blazed high and wide when well placed to ensure Moore once again left Bramall Lane with all three points.
Sheffield United: Henderson; Basham, Egan, O’Connell; Baldock, Norwood, Duffy (Washington 76), Fleck (Coutts 58), Stevens (Johnson 89); McGoldrick, Sharp. Unused substitutes: Stearman, Moore, Smith, Cranie.
West Bromwich Albion: Johnstone; Adarabioyo, Dawson, Hegazi, Gibbs; Livermore, Barry; Phillips, Barnes (Brunt 90), Gayle; Rodriguez. Unused substitutes: Sako, Mears, Myhill, Townsend, Burke, Harper.
Referee: J Simpson (Lancashire).