Only goals scored separated the sides heading into Monday's matchday three clash, but Austria had to win to leapfrog Ukraine and secure a top-two place along with the Netherlands.
Christoph Baumgartner's first-half goal ensured they progressed from the group stage of a European Championship for the first time and its prize is a trip to Wembley to face the in-form Azzurri on Sunday (AEST).
Although Ukraine could yet join it in the knockout stage, Andriy Shevchenko's men underwhelmed and might do well to advance as one of the four best third-placed teams with only three points and a negative goal difference.
Austria was on the front foot from the outset but created little of note until David Alaba delivered a dangerous corner into the centre of the box and Baumgartner toed his finish beyond Georgi Bushchan after 21 minutes.
Baumgartner had taken a blow to his head prior to scoring and eventually made way after going down again, but his team-mates continued to pose the greater threat and Marko Arnautovic should have done better than prod a tame effort wide three minutes before the break.
Ukraine's best first-half chance saw Daniel Bachmann slightly fortunate as his parry from Mykola Shaparenko's shot narrowly evaded Andriy Yarmolenko.
Shevchenko's side showed scant improvement after the interval, yet Austria's inability to add a second set up a nervy last 10 minutes.
Even then, Ukraine could not muster a second effort on target, their exciting play in the first two matches quickly forgotten as it failed to prey on its opponent's evident nerves.