John Egan's 93rd-minute winner earned Sheffield United a crucial 1-0 victory that kept their European dream alive and dented Wolves' in the process.
With seconds remaining at Bramall Lane, Egan found the net for the second game running with a towering header from Oliver Norwood's corner.
- £18 Premier League and Football channel offer
- Premier League table | Fixtures | Live on Sky
- How Sheff Utd and Wolves lined up
The victory - Sheffield United's second since the restart - lifted Chris Wilder's side up to seventh in the table and breathed life back into their hopes of capping a sensational season with qualification for Europe for the first time.
For Wolves, back-to-back defeats for only the third time this season leaves them sixth, seven points outside the top four after a potentially crucial blow to their bid to qualify for the Champions League.
How the Blades ignited European charge
Sheffield United and Wolves last met at Bramall Lane in the top-flight in 1976, 44 years on European qualification was on the line, and the high stakes made for an uncharacteristically cautious first period.
It took 18 minutes for either side to register an attempt, and, when it came, Rui Patricio was up to the task, gathering Oli McBurnie's near-post header.
The pace of Adama Traore in tandem with the link-up play of Raul Jimenez and Diogo Jota ensured Wolves posed a constant threat on the counter.
Jota's driving run on the half hour drew a desperate foul from Jack O'Connell, and from the resulting free-kick Ruben Neves clipped the crossbar with Wolves' first clear-cut effort on goal.
Neves looked to add to his back catalogue of spectacular goals with a long-range drive on 36 minutes, but the Portuguese's effort whistled a yard wide of the angle of post and bar.
Seventy-three per cent of Wolves' Premier League goals this season have come in the second half of matches but Sheffield United created the best openings in a second half bereft of clear opportunities.
The Blades had the ball in the Wolves net within eight minutes of the restart when captain Billy Sharp's deflected effort looped over Patricio, but the on-field decision to rule the goal out for offside was confirmed by VAR.
George Baldock looked to have spurned Sheffield United's best opportunity to claim all three points when he ghosted in front of Jonny Otto and headed wide with 13 minutes remaining, but the Blades pushed until the final seconds, and their endeavour was rewarded.
Norwood's whipped corner deep into stoppage-time was met by the rising Egan, and, three days on from scoring his first Premier League goal in the draw at Burnley, the defender doubled his goal tally with a bullet header that left Patricio flailing and the Blades daring to dream.
What the managers said…
Sheffield United manager Chris Wilder told Sky Sports: "I pulled my calf [sprinting down the touchline!].
"We were excellent, I really enjoyed watching my team play. I wouldn't have been disappointed with a draw against Wolves and the players and manager they have.
"We've been stretched by a few things, but everyone stood up to a man, took on the challenge and we played well and were brave in possession and in defence. Both aspects of the game had to be right and they were."
Wolves head coach Nuno Espirito Santo told Sky Sports: "It could have gone both ways, they had chances, we had chances.
"It's hard to create chances against Sheffield United, they press really high and that requires different things from us as a team. But we created chances with clear counter attacks where we should have done better.
"In the end it looked it was going to finish [with a point] but we didn't stay focused. We must defend better at the corner."
Nuno confirms Traore shoulder injury
Speaking in his post-match press conference, Wolves coach Nuno Espirito Santo confirmed winger Adama Traore suffered a repeat of the partial shoulder dislocation he sustained in March's victory at Tottenham.
Traore collided with Sheffield United defender Enda Stevens in the second minute of Wednesday's defeat at Bramall Lane, but played on until the 79th minute before being replaced by Leander Dendoncker.
"It's the same issue he had before," Nuno said. "Now let's see how he can overcome that. He is now in pain, but he's a strong boy. He keeps on going, fighting, jumping. It's in his mind but he is able to overcome that."
Opta stats: Battling Blades
- Sheffield United have won three consecutive home Premier League games for the first time since August 1993.
- Wolves have lost back-to-back Premier League games for only the third time this season, also doing so in September and January.
- Sheffield United are unbeaten in five home Premier League matches (W4 D1), their best home unbeaten run of the season.
- John Egan scored only Sheffield United's second ever 90th-minute winner in the Premier League, following in the footsteps of fellow defender Phil Jagielka in September 2006 against Middlesbrough.
Man of the Match - Jack O'Connell
The centre-back's first Premier League start since March 7 not only restored the defensive steel we've come to associate with Sheffield United this season, it re-established the Blades' attacking dominance down the left.
O'Connell had been given his first taste of action in the draw at Burnley, but he slotted back into the fold seamless and his presence could prove crucial in the club's bid to secure an historic finale to this fairy-tale season.
What's next?
Sheffield United host Chelsea on Saturday at 5.30pm - live on Sky Sports Premier League - before Wolves entertain Everton on Super Sunday at 12pm - live on Sky Sports Premier League.