The match looked to be coasting towards a draw before McAlinden headed in from an 81st-minute free-kick after substitute Odelusi had been shown his second yellow card in two minutes.
Wolves substitute McAlinden had earlier teed-up a fine chance for James Henry, while Dean Bowditch forced Wolves goalkeeper Carl Ikeme into a fine save as the Dons failed to end a home goal drought that stretches back to mid-February.
Michael Jacobs had the chance to put Wolves ahead just before half-time when a swift counter-attack saw him receive Nouha Dicko's pass and escape his markers only to fire weakly at Dons goalkeeper David Martin.
The game looked set to end in a draw though until Odelusi, who had replaced Matthew Kennedy just before the hour, fouled Scott Golbourne twice in as many minutes to pick up two bookings.
Wolves immediately made the extra man advantage count with Kevin McDonald's cross picking out McAlinden, who headed home the winning goal.