The world No.1 was the steady presence in a tournament full of shocks and looked to be easing through to the last four when she led by a set and 4-1 on Court Philippe Chatrier.
But the blustery conditions, which frequently made the players pause to wipe clay from their eyes, had already caused Sabalenka problems, and those only increased.
The Russian, seeded 25th, played intelligently in the biggest match of her career, repeatedly asking questions of Sabalenka, and the Belarusian simply did not have the answers.
Sabalenka, runner-up at the Australian Open, lost 11 of the last 12 games, her frustration threatening to boil over completely, and she stormed off court after a 3-6 7-5 6-0 defeat.
It is only the second time in her last 14 grand slams that Sabalenka has failed to reach at least the semi-finals, while she lost a love set for the first time in two-and-a-half years.
Her defeat, meanwhile, means there is no player left in the women's tournament who has previously reached a grand slam final.
Shnaider put her hands on her head in disbelief at the end of the match, and she said: "Honestly, I'm speechless. I'm super happy.
"Obviously today a little tough conditions with the wind. First time playing Aryna, super nervous, and first time playing in the quarter-finals of a grand slam."
Shnaider now faces Maja Chwalinska, who has continued her dream run at the French Open by reaching the semi-finals with a 7-6(3) 6-3 victory over Russia's Anna Kalinskaya.
The 24-year-old absorbed the power of the 22nd seed superbly, repeatedly forcing Kalinskaya into errors by extending rallies and making her hit one extra shot as she became only the second qualifier in the Open era to reach the Roland Garros semi-finals - and the sixth to achieve the feat at a Grand Slam.
After an early exchange of breaks, Chwalinska broke her opponent's serve again and saved two break points to move 4-1 ahead before nerves crept in, allowing Kalinskaya to force a tiebreak.
But Chwalinska, who had won only two Tour-level matches on clay before this tournament, rediscovered her composure at the perfect moment. After a tense nine-shot rally on set point, Kalinskaya sent a backhand long to hand the Pole the opening set.
Chwalinska maintained her momentum in the second set and, aided by a stream of unforced errors from Kalinskaya, raced into a 4-1 lead.
Kalinskaya snatched a break back for 5-3 but Chwalinska sealed victory in the next game on another unforced error by the Russian.
"Every single match here is kind of crazy for me, I'm very grateful," said Chwalinska, who has only dropped one set on her way to the last four.
Marta Kostyuk and Mirra Andreeva will meet in the other semi-final.
With AP
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