In what was tipped to be a frenetic knockout contest from the first whistle, Demiral needed just 57 seconds to break the deadlock at the Red Bull Arena, where an Arda Guler corner caused chaos inside the box.
Both Stefan Posch and Christoph Baumgartner failed to clear their lines before Patrick Pentz took an ineffective swipe at the ball, only palming it out straight to the feet of Demiral.
Without hesitation, the 26-year-old fired the ball into the roof of the Austria net, thereby setting a new record for the quickest goal ever scored in a men's Euros knockout match and the second-fastest in competition history.
However, Demiral fell short of scoring the fastest goal of the tournament, an honour which still belongs to Nedim Bajrami's 23-second strike for Albania against Italy, also the quickest goal ever at the Euros.
The winner of the final last-16 clash will take on the Netherlands in the Euro 2024 quarter-finals for the right to face either England or Switzerland in the semi-finals.