The former Celtic and St Johnstone striker was only in the side because of injuries as Binos boss Allan Moore opted to change the successful 4-5-1 formation to 4-4-2.
Hay, whose only previous goal this season came in a 5-2 defeat at Raith in September, played a starring role alongside the excellent Paddy Connolly as Forfar suffered a fourth straight loss.
It looked good for the Loons early on when Martin Cameron seized on slack defending to clip the ball beyond Myles Hogarth after just 60 seconds and even better when Stewart Devine turned a Darren Gribben shot into his own net after 16 minutes.
With Gribben outstanding, Forfar looked in command but Hay got one back just before the break when he chested a driven cross from namesake Paul past Francois Dubourdeau.
It was a pivotal moment in the game and Hay levelled from the spot on the hour mark after Steven Bell had been felled by the keeper, having seized on to a superb long ball from Devine.
Stirling were in control now, and Connolly thundered in his 10th goal of the season after Hay's effort had been beaten out, before Hay completed his hat-trick with an 80th-minute tap-in after a superb break from the back involving Connolly and John Fraser.