The Austrians needed a point to be sure of progress out of Group D on Tuesday (Wednesday AEST) and got off to a great start with Dutch forward Donyell Malen scoring an own goal in the sixth minute.
First-half substitute Xavi Simons set up Cody Gapko to equalise two minutes after the break, but Romano Schmid headed Austria back in front in the 59th minute.
Memphis Depay equalised with a brilliant finish in the 75th minute after a VAR check, but Sabitzer restored Austria's lead two minutes later with a fierce strike that proved to be the winner, despite a frenetic finale with chances at both ends.
Austria topped Group D thanks to France drawing with Poland 1-1 in Tuesday's other early game, the latter having already been eliminated before the match began.
Kylian Mbappe removed his protective face mask to celebrate netting from the spot against Poland. (AP PHOTO)
Kylian Mbappe scored from the penalty spot in the 56th minute on his return to the side, removing his protective mask for a broken nose to celebrate in front of France's fans.
Robert Lewandowski first had his penalty saved in the 77th minute by goalkeeper Mike Maignan - who was adjudged to have come off his line - before the Polish striker found the bottom corner with his second attempt to level the game up.
In Cologne, England advanced to the knockout stage as group winners after a 0-0 draw against Slovenia.
The result at Cologne Stadium also saw Slovenia reach the round of 16. Croatia were eliminated.
In a game of few chances, England substitute Cole Palmer could have sealed the win in stoppage time, but his shot was saved by Slovenia goalkeeper Jan Oblak.
England will play one of the qualifying third-placed teams in the round of 16 and are on the opposite side of the draw to Spain, France, Germany and Portugal.
And in Munich, Denmark advanced to the last 16 after a 0-0 draw with Serbia.
The Danes finished Group C with three points, the same as Slovenia, but ended up in second place because of a better qualifying ranking.
Denmark had most of the chances even though Serbia needed a victory to reach the next round.
And almost all of those Danish opportunities came through Christian Eriksen, who was making a record 133rd appearance for his country.
Denmark and Slovenia finished even on points, goal difference, goals scored and disciplinary points.
11°C