Venturing forward with the game deep into stoppage-time and the hosts 2-1 down, Swiss stopper Hitz proved the hero when he turned the ball home after a ricochet off Simon Rolfes had fallen into his path.
Hitz had been out of action since mid-November with a serious knee injury and he was at fault early in the game when he fumbled an initial effort from Josip Drmic, and the striker converted the rebound.
Substitute Caiuby equalised after the break before Leverkusen looked to have won it when Stefan Reinartz grabbed their second with six minutes left.
But Hitz had the last say to ensure a point apiece, as Augsburg and Leverkusen stayed fifth and sixth in the Bundesliga respectively.
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