Alloa had skipper Stuart Malcolm sent off for fouling Dene Shields after just three minutes and were 3-0 down after only a quarter of an hour. Their only comfort was that Stirling didn't quite manage to fully avenge the 7-0 defeat they suffered at Recreation Park in 1998.
The Wasps had won three on the trot but were behind in four minutes when Chris Aitken swept home the free-kick awarded for Malcolm's last-man challenge on Shields.
The hugely impressive Nathan Taggart plundered his first senior goal by ramming home a Shields cross at the far post in the 10th minute and just five minutes later Steven Bell's deflected 20-yarder beat goalkeeper Allan Creer.
Marek Tomana got in on the act after 35 minutes when he beat Creer from the edge of the area as Alloa fell apart.
The visitors stemmed the tide somewhat in the second half but they got a break on 57 minutes, when Shields appeared to be tripped in the box but instead was booked for diving by referee Alan Muir.
Substitute Dougie Wilson set up Shields for No 5 in 64 minutes, with the on-loan Gretna hitman netting at the second attempt after his initial effort had been saved. Chris Aitken should have made it six but blazed over after fine work by Colin Cramb.