In the 100th minute, referee Rob Jones pointed to the spot in controversial fashion after Wolves star Silva was deemed to have fouled George Baldock.
Ollie Norwood leathered the resulting penalty into the roof of the net as Bramall Lane exploded, giving them their first win of the season.
But it was heartbreak for Silva as the full-time whistle sounded as the striker broke into tears for giving away the penalty.
It came after a dramatic match which saw the Blades claim all three points to alleviate some of the pressure on Paul Heckingbottom.
Cameron Archer had put Sheffield United a goal up late into the contest with a brilliant 20-yard strike.
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But in the 89th minute, Jean-Ricner Bellegarde buried his own stunning strike and it looked like Wolves would be leaving Yorkshire with a point.
However, there was a late twist as Baldock wriggled his way into the box before Silva collided with the Greece international.
It looked like the full-back was already on his way down, though, but VAR ruled there was nothing wrong with the decision and the penalty stood.
And Norwood made no mistake as the Blades captain smashed his penalty into the top of the goal, sending the home crowd into a frenzy.
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While it gave Sheffield United a huge win at the bottom of the table, Gary O'Neil was furious with yet another VAR decision that went against him.
Wolves were the victims of a poor decision last week in a 2-2 draw against Newcastle when Hwang-hee Chan was adjudged to have fouled Fabian Schar in the box.
However, despite watching TV replays of the challenge that showed no contact and referee Anthony Taylor was relegated to the Championship as a result.
Speaking on talkSPORT, Dean Ashton could not believe that Sheffield United were awarded a penalty.
"This is exactly the same as it was last week against Newcastle," he said live on air.
"Fabio Silva looks as if he's going to clear it, Baldock puts his leg across hoping for contact, we're in the last seconds of the game and he wants a penalty, which it's going to be.
"But, I'm sorry, Fabio Silva stops just at the last second and Baldock goes over, that's not a penalty! Baldock is looking for it and throws himself over.
"It's a gigantic goal for Sheffield United and their season, but I'm telling you, that is not a penalty.
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"Referees have got to understand when players are trying to win a penalty, and this was one of them.
"Wolves, once again, have been done!"