In a tie that pitted the unexpected Group D winners against the Group F runners-up, Vincenzo Montella's side - without inspirational midfielder Hakan Calhanoglu - took the lead courtesy of Merih Demiral scoring the second-fastest goal in Euros history, netting inside just 57 seconds.
Das Team's response was bright before becoming futile for the remainder of the first half, and they were undone by another Arda Guler corner to Demiral early in the second 45 before substitute Michael Gregoritsch set up an unmissable finale.
Turkey were camped inside their own half in the final 20 minutes as Ralf Rangnick's men threw the kitchen sink at them, but a combination of dogged Turkish defending and wasteful Austrian deliveries ended the Crescent-Stars' 16-year exile from the Euros quarters.
For Austria, a quarter-final place still eludes them as they are left to rue their second straight last-16 exit, although Das Team can reflect on the green shoots of positivity from their Euro 2024 campaign as Turkey prepare for a date with the Dutch.
Demiral makes Euros history inside first minute
Many had backed the final last-16 tie of the Euros to be a chaotic affair brimming with early goalmouth action, and the first five minutes - or 57 seconds to be more precise - certainly lived up to the pre-game hype.
Unsurprisingly, Arda Guler was the instigator - albeit in more unorthodox fashion than usual - as his seemingly harmless corner deflected off of Stefan Posch and Christoph Baumgartner before falling into the path of Patrick Pentz.
However, rather than gather the ball with both hands, the Austria number one weakly palmed it straight into the corridor of uncertainty, where Demiral reacted quickest to fire in the deadlock-breaker inside just 57 seconds.
The 26-year-old now boasts the quickest knockout goal in the history of the men's Euros, and he would also hold the overall record had Albania's Nedim Bajrami not struck inside 23 seconds against Italy in the group stage.
Majestic Mert Gunok save breaks Austrian hearts
After Demiral notched his second of the contest and Gregoritsch halved the Austrian arrears, it was backs against the wall as far as Turkey were concerned in the final quarter of the match, as they repelled attack after attack.
For the most part, Demiral and his centre-back partner Abdulkerim Bardakci were unbeatable, but the pair had their hearts in their mouths in the fifth minute of added time, where Baumgartner rose highest to send an eight-yard header towards goal.
However, right when Turkey needed him to produce the spectacular, goalkeeper Mert Gunok came up with what should be remembered as one of the saves of the tournament, springing himself to the right and parrying the ball behind for a corner, which came to nothing as Montella's men collapsed to the turf in ecstasy.
Time to move on from Marko Arnautovic
Rangnick's decision to give Marko Arnautovic the nod in the number nine spot was a bold one, and one that did not pay off whatsoever, as the former Stoke City man cut an often anonymous figure in the first half.
A golden chance to get Das Team back in the tie also passed Arnautovic by in the second period, where he tried to delicately side-foot the ball past Gunok rather than lifting the ball over his Turkish compatriot, who of course came out on top.
Gregoritsch, in contrast, made the impact inside 10 minutes that Arnautovic could not do in 90 in Leipzig, and while the 35-year-old former may still be kicking by the time the 2026 World Cup rolls around, his poor display and Gregoritsch's fine cameo should signal the passing of the torch.
What next for Austria and Turkey?
In their first European Championship quarter-final since their magical run to the semis in 2008, Turkey will pit their wits against the Netherlands in Berlin on Saturday, for the right to battle either England or Switzerland in the last four.
As for a disconsolate Austria outfit, manager Rangnick remains under contract with the national team until the summer of 2025 and is therefore set to lead Das Team into their 2026 World Cup qualifying period and Nations League campaign, where they will face Norway, Slovenia and Kazakhstan in League B Group 3.