This was Albion's third win in a row and their first victory at Recreation Park since 1990 but it is Alloa's statistics that should most concern Hendrie - 10 games have passed since their last win, ironically against Stirling back in August, and 17 goals have been conceded in their last four home matches.
Goalkeeper James Evans was clearly to blame for Stirling's opening two goals, the first a long-range effort from Chris Aitken which he somehow allowed to squirm under his body, and the second a harmless-looking Paddy Connolly header which left Evans frozen like a statue.
Connolly, Ross Forsyth and Dougie Wilson all went close to a third goal and top scorer Connolly finally supplied it shortly before half time with a flashing header from Paul Nugent's cross.
David O'Brien stayed just on side to make it 4-0, and the visitors were so much on top that they could even afford to blow a three-man advantage when Alloa's defence was caught upfield at a corner kick.
Home striker Andy Brown headed two late consolation goals as Stirling let their concentration slip.