And world number two Aryna Sabalenka pummelled American Emma Navarro 6-2 6-3 in just over an hour to stay on course for her first title in Paris.
After a sluggish start on Monday with both players dropping serve, Russian-born Rybakina upped her level and cruised through the first set.
In the second set, the 29-year-old Svitolina was no match again for Rybakina as the 19th-ranked Ukrainian showed signs of fatigue from the start and lacked precision throughout.
Odessa-born Svitolina had reached the quarter-finals four times before, including 2023, but was unable to trouble the former Wimbledon champion.
Rybakina, who made the last-eight for the first time since 2021, faces the winner out of 70th-ranked Russian Elina Avanesyan and 15th-ranked Italian Jasmine Paolini.
Sabalenka, unbeaten now in 11 straight matches at the majors this year without losing a set, completely overpowered Navarro with her thundering baseline game and attacked the American's weak second serve at every opportunity.
Navarro had stunned the Belarusian at Indian Wells in March but Sabalenka broke her to love at the very start and followed that with another break to race through the first set in 30 minutes.
"It was really tough against her in Indian Wells," Sabalenka said.
"I was ready for a tough match, to fight for any point, for long rallies. I am super happy with the level I played today."
On a day of glorious sunshine, Sabalenka secured an early break in the second set courtesy of one of her 36 winners to go 2-1 up and leave Navarro with a mountain to climb.
The American managed to stay alive a little longer but could not avoid the inevitable, with the 26-year-old Belarusian, looking to add to her two Grand Slam titles so far, wrapping up proceedings on her first match point.
She will face either Varvara Gracheva of France or teenager Mirra Andreeva in the last eight.
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