However, the Yorkshire side could count themselves extremely unfortunate at the nature of Albion's 18th-minute opener when Nick Montgomery was punished for an innocuous handball.
The talismanic Graham Dorrans, who was the heartbeat of West Brom's midfield, slotted home the resulting penalty before Roman Bednar netted his third goal in five games to cap a professional first-half display.
Darius Henderson scored from the spot himself within minutes of the restart, but Jerome Thomas extinguished any hope of a fightback when he restored Albion's two-goal advantage within a minute.
The Baggies went into the clash having lost just two of their last 15, although having been leapfrogged into second place by Nottingham Forest, while United themselves had only been beaten twice in their last 14.
And both sides looked bright in the opening stages with Thomas and Richard Cresswell seeing efforts well blocked at either end.
Yet it was livewire Dorrans, recently linked with a host of top-flight clubs until penning a new deal this month, who was proving a constant threat.
And it was he who created the opener when, under pressure from Montgomery, referee Mick Russell harshly adjudged the United midfielder to have handled the ball.
The decision was extremely tough on the visitors but Dorrans stepped up to slot home the resulting spot-kick.
From then on it was all Albion and Bednar somehow side-footed wide soon after with a second goal at his mercy.
But he made no mistake just after the half-hour by converting a perfect example of counter-attacking football, although United boss Kevin Blackwell will have been fuming with the ease in which his defence were cut apart.
A visiting corner broke down and Albion right-back Gonzalo Jara switched the play to Bednar on the halfway line, he interchanged passes with Thomas and before Blades keeper Mark Bunn could react the ball was nestling in his net.
Albion were then controversially denied two more obvious handball decisions than the one that was given, before Bednar wasted a glorious chance to make it 3-0 when he latched onto Stephen Quinn's short backpass but could only find the side netting.
Such is the nature of West Brom's inconsistency this season that the third goal was always going to prove crucial.
And it was they who shot themselves in the foot just minutes after the restart when Youssouf Mulumbu hacked down Quinn in the area and Henderson smashed home the resulting penalty for his 11th league goal of the season.
But it took the Baggies just 53 seconds to hit back.
Dorrans was again the provider, launching a long ball upfield towards Thomas who jinked his way into the area before seeing his goalbound effort deflected past the helpless Bunn.
Albion showed plenty of composure from then onwards and it was they who could have added to the scoreline.
Jonas Olsson was fortunate to get away with a foul on substitute, and former Wolves man, Henri Camara late on. But the visiting fans were left travelling back up the M1 wondering what might have been had it not been for Albion's controversial opener.
Source: Team Talk
Source: Team Talk