Christoph Baumgartner scored the only goal of the match in the 21st minute as Wunderteam advance to a Round of 16 match against Group A winner Italy on Saturday at Wembley Stadium.
Ukraine must now wait to see if they are one of the four best third-place teams to earn a spot in the knockout stages after suffering two defeats out of three Group C matches.
Story of the match
Marcel Sabitzer then shot wide off of a deflection and Marko Arnautovic flashed across the Ukraine box only to fire off of a defender before Austria opened the scoring.
The excellent David Alaba sent in his fifth corner kick of the match and he picked out Baumgartner in the middle of the box, who stuck his leg out to poke home past Yellow and Blue goalkeeper Heorhiy Bushchan.
Corner kicks were still an issue for Ukraine and they were fortunate not to be two goals behind after Alaba picked out Martin Hinteregger, the Eintracht Frankfurt center-back heading wide.
In the 29th minute, Mykola Sharapenko squared up his defender then beat him inside to lash a shot into the far corner that Bachmann dove to shove away.
Austria were soon back on the front foot, Konrad Laimer darting inside Oleg Karavaev before cracking a curling, right-footed shot that Bushchan could only push away.
Wunderteam should have doubled their lead three minutes before halftime as Sabitzer clips a pass down the right for Alessandro Schopf, whose low cross finds Arnautovic, but he could only stab it wide.
Ukraine had a few good passages of play as right before halftime, Ruslan Malinovskiy slid in Roman Yaremchuk, who prodded it behind and just after the restart, Yarmolenko swung in a free-kick that Florian Grillitsch headed clear.
Schlager then saw Bushchan save his shot before going wide with his next effort. On 61 minutes, the match was nearly level following a Lainer header that he accidentally crashed against his own goal from a Viktor Tsygankov cross, Bachmann alert to push out.
Three minutes from time when Yaremchuk dashed outside Hinteregger, sending a cross shot that narrowly goes wide, the Yellow and Blue hopes fading while Austria saw out an excellent performance to deservedly move on the knockout stages for the first time in their history.
Man of the Match: David Alaba
Was the architect of all of Austria's build-up play from corners with his accuracy and ability to pick out his teammates. His experience also played a crucial role in determining the outcome.
Austria impressive, but could have won by a bigger margin
Although Ukraine put very little pressure on them and barely posed a threat, Wunderteam were solid defensively and up for it on the counterattack. Had they taken their chances, this could have been 3-0 or 4-0.
Ukraine flat throughout
Knowing they only needed a draw to reach the Round of 16, the Yellow and Blue were pretty much lethargic from start to finish. They never got a clear sight of goal, never broke down the Austria defense and didn't test Bachmann. They must now wait to see how the rest of the group stage matches play out before their fate will be determined.