The last-16 game went to a shootout on Monday (Tuesday AEST) because Ronaldo's extra-time spot kick in the 114th minute was saved by Slovenia goalkeeper Jan Oblak. Regulation and extra time had finished 0-0.
When they went to penalties, Ronaldo scored his and Portugal's first, and teammate Diogo Costa saved all three of Slovenia's kicks, from Josip Ilicic, Jure Balkovec and Benjamin Verbic.
Portugal's goalkeeper Diogo Costa saved all three penalty attempts by Slovenia. (AP PHOTO)
Bruno Fernandes and Bernardo Silva also scored for Portugal to seal the shootout 3-0 with two shots to spare.
Portugal will face France in the quarter-finals on Friday in Hamburg, a rematch of the 2016 final that Portugal won in Paris.
Costa had already made his first save when Ronaldo walked up to take Portugal's first kick of the shootout, and placed it perfectly low beyond Oblak diving to his right.
Ronaldo looked apologetically to the massed Portugal fans behind the goal and put his hands together as if in prayer. The fans responded with a bellowing shout of "Siuuuu" - their soccer icon's trademark goal scream.
Costa answered the rest of those prayers with as good a penalty shootout as any goalkeeper ever had. Then he was in tears, too.
A half-hour earlier, Ronaldo was distraught and crying at halftime in extra time after his penalty was saved by Oblak, diving to his left to push the ball against a post.
Portugal's Cristiano Ronaldo was reduced to tears after missing a penalty against Slovenia. (AP PHOTO)
It had been the latest victory for Oblak in their personal duel during a compelling 90 minutes of regulation time.
The intense extra-time drama followed an intensely frustrating first 90 minutes for Ronaldo, who was still looking for his first goal at Euro 2024.
After three free kicks and two mistimed headers, the Portugal star seemed sure to score with his first clear shooting chance in open play.
It came in the 89th minute, when he ran clear on goal with the ball passed perfectly into his stride. The left-foot shot was low and powerful, but Oblak's block was better. Ronaldo held out his arms in exasperation yet again.
The intense drama for the Portugal superstar almost overwhelmed the troubled evening for Slovenia's emerging star.
Benjamin Sesko had golden chances to win the game, in the 62nd and 115th minutes, going one-on-one with Portugal goalie Costa after racing past 41-year-old defender Pepe.
The first was a weak shot that screwed wide of goal, and the second was powerful and accurate and saved by the outstretched boot of Costa.
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