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.
1. Illan Meslier
7 - Looked unsighted and helpless for the goals. Played well enough before being clattered and injured by Jimenez. Photo by Laurence Griffiths/Getty Images.
2. Luke Ayling
8 - A leader's performance in the second half. One of those we've seen before when he gets the bit between his teeth. Photo by GEOFF CADDICK/AFP via Getty Images.
3. Diego Llorente
6 - Looked shaky at times before picking up the knock that forced him off. Photo by Laurence Griffiths/Getty Images.
4. Pascal Struijk
7 - Had to do some important defending in the second half alongside Cresswell. Photo by Laurence Griffiths/Getty Images.