Goals from midfielders Rodri and Fabian Ruiz brought Spain back into the game after Robin Le Normand's own-goal in the 18th minute had given Georgia a shock lead in Cologne.
Nico Williams and Dani OImo put the game out of Georgia's reach with two more goals late in the game as heavy rain fell.
After the final whistle, Williams and 16-year-old Lamine Yamal met up on the field for an impromptu game of rock-paper-scissors, apparently over who got to drink first from a water bottle.
It was a moment that summed up the unpredictability and sense of fun in a Spain team that had previously been prone to retreating into an unthreatening passing game, as in their loss to Morocco at the same stage of the 2022 World Cup.
Rodri said facing Georgia was a test of Spain's nerves.
"It was a tough game. We knew it before. Maybe they don't have the big names, but they made it hard for us," he said, adding that his goal "was key because we were a bit jittery at that point… We have things to improve."
Spain will play hosts Germany in the quarter-finals on Friday (local time) in Stuttgart.
"Obviously Germany at home is going to be very strong, but we have no fear. We have our own weapons," Rodri said.
The loss ends Georgia's first major tournament campaign, which included a 2-0 upset win over Cristiano Ronaldo's Portugal.
Despite the lopsided score on Sunday (Monday AEST), Georgia goalkeeper Giorgi Mamardashvili had another standout game with nine saves to prevent a rout.
Spain had beaten Georgia 7-1 in qualifying last year, but this game was a close contest until the last 20 minutes and testament to Georgia's rapid improvement under coach Willy Sagnol.
Georgia players acknowledged their fans after bowing out of Euro 2024 with a 4-1 loss to Spain. (AP PHOTO)
Playing their fourth game of Euro 2024, Spain had yet to concede a goal all tournament.
That soon changed when Otar Kakabadze surged down the right flank for Georgia and crossed low. Le Normand chested the ball past his own goalkeeper, with the defender apparently distracted by Khvicha Kvaratskhelia arriving behind him to meet the cross.
Spain took their time to get back into the game, but Rodri - back from a one-game suspension - levelled the scores in the 39th minute with a low shot from just outside the box.
Georgia remained a threat on the counter, including with an audacious shot from the halfway line by Kvaratskhelia, but Spain midfielder Ruiz made it 2-1 in the 51st minute when he rose unmarked to meet a cross from Yamal.
Needing a goal, Georgia had to open up their compact defensive formation and conceded twice more, with Williams scoring in the 75th minute and substitute Olmo eight minutes later.
Georgia coach Sagnol said his team could have beaten Spain after Le Normand's own-goal, but the combination of the equaliser from Rodri and an injury to Otar Kiteishvili just after took the wind out of their sails.
"We thought we could have a chance," Sagnol said. "We did lose a lot in these 20, 30 seconds."
After the final whistle, Georgia's players gathered in front of their fans for a slow-clap chant reminiscent of another European Championship underdog - Iceland - when they beat England in 2016.
Spain have won two of their three previous meetings at the Euros with Germany, the last match their 1-0 victory in the 2008 final.
The two sides drew 1-1 at the 2022 World Cup, and four years ago Spain thrashed Germany 6-0 in the Nations League.
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