Real Madrid midfielder Arda Guler crashed in a brilliant goal in the 65th minute at a Westfalenstadion dominated by tens of thousands of Turkey supporters before Kerem Akturkoglu rolled home the third deep in stoppage time as Georgia pushed for a late leveller.
Guler, 19, had a difficult time with injuries in his first season in Madrid but stepped up for Turkey in a fiercely-contested match with Georgia, who did not look out of place in their first-ever match at a major international tournament.
Georgia were dangerous after Georges Mikautadze levelled Mert Muldur's 25th-minute opener for Turkey just after the half-hour mark, and were denied a second equaliser by the woodwork and a series of saves and blocks.
But Akturkoglu made sure Turkey would top the group ahead of Portugal's opening match with the Czech Republic later on Tuesday.
Turkey took the cue from their fervent support and went at Georgia from the off, pressuring their inexperienced opposition high up the pitch as a huge din came rolling down the stands.
Kaan Ayhan and Abdulkerim Bardakci both went close with headers from corners inside the first 10 minutes before Ayhan crashed a low drive off the inside of the post.
And in a breathless opening period Anzor Mekvabishvili almost gave Georgia a shock lead in the 11th minute when his wildly deflected shot was well saved by Mert Gunok.
But Muldur sparked wild celebrations in the stands in the 25th minute with a stunning volley after Ferdi Kadioglu's cross was cleared to him on the edge of the area.
Brave Georgia
The roars from Muldur's goal had barely subsided when Kenan Yildiz poked home what he thought was Turkey's second, only for the goal to be ruled out for the Juventus attacker's toes straying offside before he tapped home.
And Mikautadze stunned what was effectively the home crowd in the 32nd minute by sweeping home Giorgi Kochorashvili's low cross after brilliant play down the right.
The small but loud Georgian contingent had their heads in their hands shortly afterwards when Mikautadze look certain to put their team ahead but dragged a great opportunity wide.
Turkey again started in the front foot after the break but Georgia held their own and Mikautadze was in the thick of it again in the 52nd minute when Bardakci blocked his effort after Khvicha Kvaratskhelia's burst down the left.
Kvaratskhelia, who was below-par throughout, then poked a good chance wide in the 62nd minute and only moments later Guler took aim from distance and arrowed in an unstoppable shot past the despairing Giorgi Mamardashvili.
Georgia pushed for another equaliser and came desperately close five minutes after Guler's strike when Kochorashvili skipped past a couple of weak challenges only to see his shot rattle the crossbar.
But Kochorashvili and Zuriko Davitashvili were both unfortunate not to level in added time as Mamardashvili pushed forward for one last effort and Akturkoglu charged home on the break to seal a thrilling win.
