The eastern European nation with a population of four million, playing in a major tournament for the first time, registered the biggest win in their existence as goals from Khvicha Kvaratskhelia and Georges Mikautadze in either half ensured they finished third in Group F.
That saw them qualify for the last 16 where they will play Spain, while Portugal meet Slovenia.
Portugal’s position as Group F winners was secured with wins in their opening two games, so boss Roberto Martinez made eight changes to his starting XI.
And they were caught cold as Georgia, ranked 74th in the world, stunned them by taking the lead after just 93 seconds.
Benfica defender Antonio Silva will not want to see a replay of the goal as his wayward pass went straight to Mikautadze who advanced and played in Kvaratskhelia to finish across goal into the bottom corner.
Portugal quickly assumed dominance and peppered the Georgia goal with shots.
Cristiano Ronaldo had a trademark swerving kick saved by Giorgi Mamardashvili while Joao Felix curled an effort just wide.
Ronaldo almost equalised early in the second half as his shot from close range was deflected, but Georgia’s defence was brilliantly resolute.
The pivotal moment of the game came just before the hour mark as Silva’s night went from bad to worse.
Luka Lochoshvili burst into the area and went down under a wild swing of the leg from Silva.
Referee Sandro Scharer waved play on and Portugal raced forward, with Mamardashvili producing a stunning save to keep out Diogo Dalot’s effort.
But in the break of play VAR told the Swiss official to check the monitor and he awarded a penalty with Mikautadze slotting home to give Georgia a crucial two-goal advantage.
Georgia, managed by former France international Willy Sagnol, had 20 minutes to see out and create history and they did it relatively trouble free.
They were the team who looked most likely to add to the scoreline with Mikautadze blazing over on the counter attack and Zuriko Davitashvili hitting the side-netting.
They saw out a nervy stoppage-time period, where Portugal came close to scoring, but they held on to claim a stunning win, with 68 places between the two countries in the rankings.
