The Blades went behind within the first 15 minutes, to a Mikael Arteta header, and their fate was sealed just after the half hour mark when defender Claude Davis was given his marching orders for hauling down Andrew Johnson in the box - James Beattie doubling the lead from the resultant penalty.
Despite Warnock's claims that his side are still trying to bridge the class divide in their new surroundings this will have been a game the United manager would have wanted something out of.
Everton, without a win in three games, were low on confidence at kick-off, a fact proved by their inability to string more than a couple of passes together in a cagey first ten minutes.
But after Arteta's goal the Blues were in complete control and despite Warnock's admirable attempts to give his side a chance, with a number of tactical reshuffles, they rarely troubled David Moyes' men.
Arteta, Tim Cahill and Johnson were supreme for the home side, the former in particular toying with the United defence at every opportunity with some sublime passing.
His goal was testament to that as he played in Phil Neville down the right before striding forward to meet the full-back's cross six yards out with a deft header.
On that half hour mark Everton's dominance and Sheffield's misery, was compounded when Arteta's clever flick sent Johnson racing through on goal.
As the England man went to pull the trigger he was shoved aside by Davis and referee Gallagher deemed it enough to warrant a penalty and a red card.
Beattie stepped up and coolly slotted his kick to the keeper's right.
Substitute Chris Morgan could have got one back for United six minutes before the break. Keith Gillespie's free-kick found him unmarked on the back post, but the big defender directed a powerful header inches wide.
That sparked a flurry of late activity with Rob Hulse's superb run and shot almost reducing the deficit minutes later and Johnson hitting the post with a left footed drive.
United started the second half with the kind of grit and purpose that you'd expect of a Warnock side. Two minutes after the restart they almost got their reward as Mikele Leigertwood took advantage of lax play in midfield from Cahill and strode towards goal.
His shot drifted inches wide however and with that so did Sheffield's hopes of taking anything from the game.
As the effects of playing with a man less began to take their toll Everton could, and should, have added to their lead.
James McFadden was denied by a superb save from Paddy Kenny and Leon Osman should have done better after twice wriggling his way into the box.
Late on Leigertwood's timid drive dribbled wide and Warnock's displeasure was their for all to see as he stood, hands on head in the technical area.
He may well have been able to enjoy the excitement of the Premiership thus far, but many more days like this and the United boss will be back to his irate best.