The former Stockport striker converted crosses either side of the break to help condemn the visitors to a fifth successive defeat.
The Dons took the lead in the 11th minute when Jemal Johnson's corner found Sean O'Hanlon and the defender was left in acres of space to head home.
It was two six minutes later when another Johnson corner caused havoc and Wilbraham poked past David Lucas.
Leeds finally came to life and were back in the match four minutes after the break when Robert Snodgrass volleyed past Willy Gueret from 20 yards.
However, McAllister's men shot themselves in the foot five minutes later as they allowed Wilbraham more space in the box to head in another Johnson cross.