The Turkish Crescent-Stars advanced alongside Group F leaders Portugal in a 2-1 victory against Czechia on Wednesday.
Türkiye finished second in Group F after a late 2-1 win over the now-eliminated Czechs, who were hampered by Antonín Barák becoming the second man in Germany to be dismissed after two harsh first-half bookings.
Türkiye captain Hakan Çalhanoğlu scored in style on 51 minutes, with Czech goalkeeper Jindřich Staněk appearing to dislocate his shoulder moments before the goal.
The Czechs hit back on 66 minutes through their own skipper TomášSouček, but it was not enough for the win they needed as Cenk Tosun scored in stoppage time of a bad-tempered affair.
Ivan Hašek's side, who started without injured striker Patrik Schick, faced the ignominy of seeing former smaller partners Slovakia qualify for the last 16 earlier, a day after Slovenia had gone through as former big brothers Serbia and Croatia were dumped out.
A draw was enough for Türkiye to advance as group runners-up, a position that guarantees a spot in the last 16.
Their 3-1 victory over Georgia in the opener meant they only needed a single point to progress.
Impressively, they have lost only three of their last 16 competitive matches, showcasing their resilience and determination.
Georgia also qualified for the Euro 2024 last 16 in their first major tournament.
Portugal, the 2016 champions, had already won the group and their much-changed side lost 2-0 to Georgia after Khvicha Kvaratskhelia gave them a shock lead after just 2 minutes.
Tournament top scorer Georges Mikautadze then netted his third at these Euros from the spot in the second half to spark ecstatic scenes among fans of a nation gripped by political protest at home.
The surprise win, Georgia's first at the Euros, sets up a dream meeting with Spain and means they progressed as one of the four best third-placed sides alongside Slovenia, the Netherlands and Slovakia.
Hungary, who have been waiting in third place on three points since Group A concluded on Sunday, are now eliminated on goal difference. Croatia, third in Group B, were previously ruled out of contention.