Kazakhstan's Rybakina recovered from 0-3 and two breaks down in the final set to beat Liudmila Samsonova 6-4, 4-6, 6-4 before American Gauff swept aside another Russian, teenage qualifier Alina Korneeva, 6-3, 6-1 in Toronto.
Rybakina will face a quarter-final against four-time Grand Slam champion Naomi Osaka, who eliminated home hero Leylah Fernandez 6-4, 6-4.
Gauff reached the last eight in Canada for the first time since 2023 and next meets 14th-ranked Swiss Belinda Bencic, who won 6-4, 6-0 in 73 minutes over 20th-ranked Alexandra Eala, a Filipina who won her first WTA title last Monday in Washington.
"My main focus today was let me try and close it out," said Gauff, who has not dropped a set in Canada.
"Probably not the way I should be thinking but it worked today.
"I'm proud of how the last three matches have gone and just knowing if I have to go the distance I'm ready but obviously would prefer to cut it short if I can."
Osaka broke in the seventh game of each set to advance in 82 minutes.
"It was all pretty good for me," the 13th-ranked Osaka said. "She has a great attitude. She's consistent and she will fight. She's kind of like a bulldog."
The Japanese star, who has never faced Rybakina, said sound groundstrokes were key.
"When I feel comfortable or at least confident in myself knowing I can run things down, I loosen up a lot," Osaka said.
"I was catching my service toss a couple times. Hopefully in the next match I don't do that as often.
"I need to be confident in myself, execute what I can and at the end of the day just try my best and whatever happens happens."
Bencic connected on 64.4% of her first serves and won 72.4% of those points in a 73-minute victory, her 10th win in a row over left-handed opponents.
"I hate to play against lefties so I'm surprised by this statistic," Bencic said. "Very tricky.
"Maybe helped me I played a lefty the round before against Taylor Townsend. I got used to the serve a little bit. I wish I was a lefty too."
