Whites duo Rodrigo and Jack Harrison scored in the 63rd and 66th minute to draw Leeds level after going in at the break two goals and three injured players down.
Strikes from Jonny and Francisco Trincao had Wolves 2-0 up at the interval, by which point United had already lost the services of Patrick Bamford, Mateusz Klich and Diego Llorente who all had to be taken of.
A hefty collision between Raul Jimenez and Illan Meslier early in the second half spelled readjustment for both sides as the players were taken out of the game - Jimenez dismissed for a second yellow.
Meslier was replaced by Under 23s shot-stopper Kristoffer Klaesson as Jesse Marsch could use a fourth substitute following the removal of Klich under concussion protocols.
A wild evening then took one final twist in the 91st minute as Leeds completed a sensational comeback when Luke Ayling slammed home a clinical finish from inside the box.
Graham Smyth, the YEP's chief football writer, hands out the scores following a scarcely believable turn of events at Molineux.
7. Mateusz Klich
6 - Some tidy bits of play but couldn't really get into the game as he would have wished. Horribly unlucky for the injury. Photo by GEOFF CADDICK/AFP via Getty Images.
8. Dan James
7 - Caused problems but composure was lacking at times. Unlucky not to score, hit the woodwork. Photo by Naomi Baker/Getty Images.
9. Jack Harrison
7 - Produced some decent crosses late on, scored a hugely important goal. Won't have been happy with what he produced in the first half. Photo by GEOFF CADDICK/AFP via Getty Images.
10. Rodrigo
8 - Wanted the ball, got into good positions to receive it. Not everything he tried worked but he showed the necessary desire and got his goal. Photo by Naomi Baker/Getty Images.
11. Patrick Bamford
6 - Looked distraught when he came off. Had missed a good chance but not really got into it. Picture by Bruce Rollinson.
12. Sam Greenwood (sub)
7 - Worked hard. Struggled to make an impact at times against vastly experienced defenders but did enough. Photo by Laurence Griffiths/Getty Images.