Leverkusen led for the first time when Maximillian Wagener latched onto a stray pass in midfield and advanced to stroke the ball wide of Gollini.
To their credit, United hit back when Sam Byrne had a shot saved and Pereira was on hand to rifle in the rebound to make it 3-3. Both teams had chances, Henrichs seeing a header clawed away by Gollini, and Wilson speeding through only to shoot against Schnitzler's legs before a second yellow card saw McNair sent off with quarter of an hour remaining.
Louis Rowley made a vital block to frustrate Francesco Gibaldi as the Reds withstood the inevitable late pressure and Wilson came up trumps with a minute remaining, using his pace to outstrip Marlon Frey and being sent crashing to the ground. Wilson dusted himself down to blast home the winner from 12 yards to seal a memorable triumph.
United: Gollini; Weir (Willock 69), McNair, Ioannou, Rowley; Pearson (Harrop 69), Grimshaw, Rothwell, A.Pereira (Evans 86); Byrne, Wilson. Subs not used: J.Pereira, Fletcher, Barber.