John Ovenstone forced a rebound from an Iain Nicolson shot past Myles Hogarth in the Albion goal, but he was adjudged to be fractionally offside.
Stirling Albion's defence absorbed the Alloa pressure and in the 20th minute they had a golden opportunity to take the lead when Paul Hay fired in a fierce 25-yard shot only to see it brilliantly saved by James Evans.
Their pressure however was rewarded in the 21st minute when they took the lead after Paul Nugent on the edge of the penalty box connected with a Hay corner and through a packed Alloa defence beat Evans.
Stirling were forced into the 38th minute when they lost the services of Paul Di Giacomo following an act of violent conduct when he struck Michael Bolochoweckyj on the face with the match ball.
Alloa came close to equalising in the 33rd minute when Ovenstone's long throw-in reached the feet of Ross Hamilton, but from six yards out he somehow managed to blast the ball over the bar.
Alloa started the second half strongly and they richly deserved their equaliser in the 55th minute when Ovenstone's long throw into the Stirling penalty area outwitted the defenders and Chris Townsley ran in to fire home past Hogarth.
Neither side in the closing minutes of the match were able to break through and snatch the winner and in the end a draw was a fair result.