But this was just the tonic Paul Heckingbottom needed after a harrowing start to the campaign on their return to the top tier and they are now just two points off safety after Burnley and Bournemouth lost again.
There was more penalty woe for Wolves, following on from last week’s controversy against Newcastle, but their five-match unbeaten streak came to an end.
The sodden conditions made for a chaotic opening, where Wolves looked the most likely as they regularly found space down their right-hand side.
Hee-Chan Hwang looked dangerous and forced Wes Foderingham into a flying save before the South Korean was involved in the best opening of the first half in the 32nd minute.
He wriggled clear in the box and looked primed to score but skewed his shot straight into the path of Rayan Ait-Nouri, who could not turn the ball goalwards.
Sheffield United improved immeasurably after the break and boxed Wolves in for the first 20 minutes.
Just as it looked as if Wolves had weathered the storm, the Blades went ahead in the 72nd minute with a moment of quality.
There was some fortune in how it came about as a clearance from Cunha hit McAtee and sent Archer clear but from then on it was all about the former Aston Villa striker.
As it looked like he might be caught by the chasing Wolves defenders, Archer unleased a 25-yard shot that arrowed in off the underside of the crossbar.
But the Blades appeared to suffer more disappointment in the 89th minute when Bellegarde’s effort deflected off Baldock and over Foderingham, who got a hand to it.
There was late drama as Silva went through the back of Baldock deep into time added on and after the decision by referee Rob Jones survived a vigorous VAR check, Norwood smashed the spot-kick in off the crossbar to send Bramall Lane into raptures.