Christoph Baumgartner - who later went off with a head injury that appeared to be sustained before he scored - netted the only goal of the game as the two sides met in a straight shootout in the Romanian capital of Bucharest on Monday evening.
That was enough to secure Austria’s passage through to the last 16 as Group C runners-up behind the Netherlands, who were already guaranteed top spot before their 3-0 triumph over North Macedonia in Amsterdam.
Ukraine needed only a point to guarantee progression and - with only three points in the bag - now face a nervous wait to discover if they will be able to seal one of those coveted four best third-place finisher spots.
However, a negative goal difference is likely to count against them in that respect.
For Austria, second place in Group C means they face a last-16 showdown with formidable Group A winners Italy at Wembley Stadium in London on Saturday evening.
It should prove an incredibly tough occasion for Franco Foda’s side, with the Azzurri now unbeaten in their last 30 matches across all competitions.
Indeed, Italy have won each of their last 11 games without conceding under Roberto Mancini - a run that includes successive Group A wins over Turkey, Switzerland and 10-man Wales on home soil at Rome’s Stadio Olimpico.
The Austrians last made it through to the knockout phase of a major tournament at the 1982 World Cup in Spain - an achievement that was heavily tainted by the infamous ‘Disgrace of Gijón’.