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.
13. Robin Koch (sub)
7 - Got stuck in. Played a lovely ball for Ayling that eventually led to a goal. Photo by GEOFF CADDICK/AFP via Getty Images.
14. Charlie Cresswell (concussion sub)
7 - A couple of moments of head-loss aside he dug in and threw himself at the challenge. Photo by Laurence Griffiths/Getty Images.
15. Kristoffer Klaesson (sub)
8 - The coolest man in the heat of battle. Made two big saves, one of them world-class, punched a dangerous cross clear. Photo by Naomi Baker/Getty Images.
16. Kevin Friend (referee)
6 - Missed a bad one on Dallas, wasn't helped by VAR there. Struggled to keep a lid on it with so much to do. Largely consistent. Photo by GEOFF CADDICK/AFP via Getty Images.