The vital goal came on 13 minutes when a Craig Sibbald corner was nodded down by Conor McGrandles and Loy diverted the ball over the line with a back-heel.
Hibs almost levelled when Farid El Alagui slipped a pass to Paul Heffernan, but Falkirk keeper Jamie MacDonald blocked the shot.
El Alagui then sent a header against the bar after Michael Nelson won a header at the back post from a Hibernian corner.
At the other end Mark Oxley saved a lo9w drive from Loy, but Blair Alston squandered the rebound.
The Hibernian keeper then got down to turn another effort from Loy, turning his angled drive round the post.