Austria made a fast start to proceedings, Rangnick's fast and aggressive style on full display, and they were ahead inside 10 minutes when centre-back Trauner sent a fine header beyond Wojciech Szczesny.
But, to their credit, Poland were able to soak up Austria's continued pressure and found a way back into the game on the half-hour mark. Rangnick's side failed to clear a corner and Krzysztof Piatek reacted quickly to fire a loose ball home.
Poland introduced Robert Lewandowski in the second half but their hopes of securing three much-needed points were dealt a blow when Baumgartner finished off a neat move to restore Austria's lead, a lead they would extend through Arnautovic's late penalty.