Stirling went into the game chasing a fourth consecutive shut-out for the first time in 11 years, but they were ripped apart in the second half on a freezing afternoon at Forthbank.
Alloa, for their part, have now won six of their last seven league matches and will be confident of another success when they host Stirling at Recreation Park next midweek.
Albion had early chances and winger Dougie Wilson blasted a 20-yarder against the crossbar before firing over when clean through.
But Iain Nicolson gave Alloa the lead with a tap-in from close range in the 37th minute after giant striker Andy Brown and Jose Quitongo combined to create the opening.
Home midfielder Kevin MacDonald was denied an equaliser by Wasps' keeper James Evans early in the second half, and Stirling were to pay dearly for that miss.
Brown set up Quitongo to score from a tight angle after 62 minutes, and the Angolan forced the ball home for the third goal with 15 minutes remaining after Ross Hamilton created the danger.
Albion's misery was complete with seven minutes left when Stewart Devine saw red for hauling down Hamilton, and John Ovenstone's free-kick deflected off the wall on its way past Myles Hogarth.