The Blades, who are still the only side in the Championship yet to score a goal, crumbled at the back, as the Baggies pressed tenaciously throughout.
Following a brilliant long-throw from Darnell Furlong, Jack Robinson lobbed the ball into his own goal in the 26th minute, to open the scoring.
A second-half overflowing with scrappy goals started began with Dara O'Shea utilizing Sheffield United's defensive error to double West Brom's lead. Alex Mowatt then slotted home a tidy finish, before Callum Robinson rounded off the scoring with a fourth. The blue-and-white side were tremendous.
But it was not just a night to forget for Sheffield United. It has been a season-opening to forget, ultimately; Slavisa Jokanovic's side need to change something up soon.
Story of the match
West Brom began the game bristling with confidence, anticipation and determination; vital ingredients if the Baggies are to realise their promotion ambitions this season. Inside the opening 70 seconds, Darnell Furlong's long throw-in found Callum Robinson at the centre of a huddle inside the box. Robinson bundled it home but the offside flag was quickly and correctly raised.
They continued to charge at Sheffield United's backline with both anticipation and aggression for the next 10 minutes, and although this resulted in no clearcut chances, the Midland side's quality was vivid. However, the Blades could not find a way to exhibit theirs.
And, in the 26th minute, West Brom discovered their treasure. Furlong, once again, hurled a lethal long-throw into the box and Sheffield United were unable to deal with it, with Blades defender Jack Robinson inadvertently nodding the ball into his own net.
The red-and-white striped side attempted to instantly respond with a goal, but this was to no avail. Billy Sharp threaded through a deft pass to strike partner David McGoldrick, who was in on goal. But the Irishman fluffed his lines and slotted it just wide of the post. He had to score.
Sheffield United tumbled into half-time fully aware that their efforts were too weak, too tame, too slight for the tribulations of the second tier. But The Baggies seemed prepared for this gruelling division, and they deserved their lead.
And just as the second half opened, West Brom doubled their advantage. A corner was whipped in and stand-in keeper Michael Verrips tapped it into the air above him. He tried to catch the plummeting ball, but he dropped it down to Dara O'Shea, who stabs it in.
West Brom were still hungry for more, though. Karlan Grant wins the ball in the final third and fizzes it to Alex Mowatt on the right-hand side of the box, who calmly prods it across goal, into the bottom left corner.
Soon after that came number four. Yet another long-throw from Furlong - West Brom's weapon of the night - was bundled into the box. It bounces past a host of bodies but Callum Robinson was at the back post to push it in.
The final 20 minutes were quiet, but neither side cared, for it was Sheffield United fans who jokingly cheered "we had a shot". The Blades' ironic inability to provide any attacking cutting-edge crafted together the story of the match.
This was an entirely deserved win for West Brom, who now have momentum, goals and points aplenty.
Man of the match - Darnell Furlong
Furlong's wonderful, precisely-inflicted long-throws paralysed Sheffield United's defence. He exposed their fragility smartly, and although his set-piece performance was crucial in this thrashing, his crossing thorned the opposition, too.
In essence, Furlong was unplayable.