In a tournament that has witnessed several shocks, including the exits of defending champion Coco Gauff and four-time winner Iga Swiatek, Sabalenka's loss sent another jolt through the wide-open women's draw.
Shnaider reached her maiden Grand Slam semi-final after an inspired battle in which she won the last 10 games having been two points away from defeat, and she takes on Polish qualifier Maja Chwalinska in the last four.
"Obviously, the first time playing Aryna, I was super nervous. The first set, I was trying to adjust to her game, trying to figure out how to play," Shnaider said.
"I feel like I was trying to focus point by point, not thinking about the score. She's the world number one, so I just tried to do my best. I just had to fight for every point.
"It's definitely a super special win. I feel in the third set I finally found my rhythm and how to play and where to be a bit more. The third set was the one I should be aiming for from the beginning. Super happy to finish on a good note."
The conditions on Court Philippe Chatrier proved a massive challenge for both players as they affected precise shot-making, but Sabalenka found her groove to open up a 5-1 advantage before she dropped serve when the wind began to really swirl.
The Belarusian let out a frustrated scream after netting a backhand to give Shnaider another breakpoint, but she composed herself again to wrap up the first set in 49 minutes and punch the air to loud applause from the crowd.
Russian 25th seed Shnaider dropped her level in the second set to fall behind again before mounting a spectacular comeback to erase a double break and level at 5-5 and drag four-times major champion Sabalenka into a decider.
Left-hander Shnaider's forehand caused all kinds of issues early in the final set for Sabalenka, and the 22-year-old broke for a 2-0 lead with a crosscourt winner before holding firm to seal the win.
Last year's runner-up, Sabalenka, cut a dejected figure after a defeat that snapped her run of six straight Grand Slam semi-finals.
With this result, there will now be a new Grand Slam winner in both the men's and women's tournaments.