Lukas Rupp put the hosts in front, but Dominik Kaiser etched his name in the history books as the scorer of Leipzig's first ever Bundesliga goal.
Mark Uth thought he had won it for Hoffenheim when he struck in the 83rd minute but Sabitzer ensured Leipzig did not go away empty-handed from their first Bundesliga outing as the 55th club to appear in Germany's top flight.
Shortly after the game was over the newly-promoted side announced the signing of Nottingham Forest's 19-year-old attacking midfielder Oliver Burke, on a five-year contract.
In the day's other game, Hertha Berlin beat Freiburg 2-1 with most of the drama condensed into the three final minutes of stoppage-time.
The hosts led through Vladimir Darida's goal against his former club - but Freiburg thought they had salvaged a point when Nicolas Hofler headed in Vincenzo Grifo's corner.
Julian Schieber had other ideas, though, and his deflected shot earned the Old Lady all three points at the Olympiastadion.
Despite just starting this weekend, the Bundesliga now takes a two-week break for international fixtures.
