Fisnik Asllani gave Kosovo the lead in the second half, but substitute Christoph Lang struck five minutes from time to rescue a point for Austria.
The result kept Austria unbeaten after four matches and left them top of Group B3 with eight points. Kosovo moved to five points in second place.
Kosovo break the deadlock
The first half ended goalless, with both sides creating opportunities without finding a breakthrough.
Kosovo eventually took the lead in the 70th minute through Asllani, who finished to put the hosts 1-0 ahead.
Austria were once again forced to respond after falling behind, having also surrendered a two-goal lead to draw 2-2 with the Republic of Ireland four days earlier.
Lang rescues Austria
Austria head coach Ralf Rangnick turned to his substitutes in search of an equaliser, and the decision paid off.
Christoph Lang came off the bench and levelled the match in the 85th minute, giving Austria a share of the points.
The late equaliser continued Austria's impressive resilience in the group, with the visitors recovering from losing positions in consecutive matches.
Austria remain top of Group B3
The draw leaves Austria at the summit with eight points from four matches.
Kosovo sit second with five points, ahead of the Republic of Ireland on account of their head-to-head record, while Israel remain fourth.
Austria will face the Republic of Ireland again in November before concluding their group campaign against Israel.
Match summary
• Kosovo: Fisnik Asllani 70'
• Austria: Christoph Lang 85'
Final score: Kosovo 1-1 Austria