Eric Asamany's goal appeared to have the Sogakope side on course fir a win but Adebayor struck with four minutes remaining to secure a 1-1 draw for the home side.
The Allies captain produced a powerful strike from range to beat goalkeeper Acquah between the sticks for WAFA.
In terms of territorial dominance, the home team were on top and first to ask a question in the match was Adebayor.
Just after the hour mark, the Academy Boys took the lead.
Eric Asamany lobbed the ball over the goalkeeper from the left side of the box, then two Allies defenders collided and the ball came off Richard Acquaah to enter the net.
After the hour, Adebayor squandered another opportunity when he shot wide from inside the box.
Four minutes from time, Adebayor's powerful strike beat the goalkeeper for the deserved equalizer.