United had the perfect start when Andrew Ferguson fired home after just three minutes.
Stirling were the better side without testing Ayr keeper Ludovic Roy, but they finally levelled at 67 minutes when Andy Gibson played in Scott McLean to shoot low past Roy from 12 yards.
Ayr then brought on Wardlaw and he made an immediate impact heading home a Craig Conway cross.
The former amateur striker then sealed the points with a wonder goal when he beat four men and sent an angled drive past Myles Hogarth.
Stirling grabbed a consolation when David O'Brien's shot crept in despite Roy's effort to save, but it was too little too late for Albion.