One of five US quarter-finalists, the 22-year-old Anisimova took a mental-health break from tennis last year. She has two WTA Tour titles - in 2019 in Bogota and 2022 in Melbourne.
"She's an amazing player, so it's always really tough playing against her," Anisimova said about Sabalenka, the Australian Open winner the last two years.
Anisimova improved to 5-2 against Sabalenka after losing the previous two matchups.
"I played her earlier this year at the Australian Open when she was on fire," Anisimova said. "I went in with a little bit of a different game plan, and I was really happy with how I was able to execute that today."
Sabalenka, from Belarus, had eight double faults in windy conditions, the last at love-40 in the final game. She withdrew from Wimbledon because of a shoulder injury and skipped the Paris Olympics
Anisimova will face eighth-seeded Emma Navarro in an all-American semi-final. Navarro beat fellow American Taylor Townsend 6-3 7-6 (7-5).
"It was really tough," Navarro said. "The wind was swirling."
Townsend was the first "lucky loser" to reach a WTA 1000 quarter-final. She got into the main draw as an injury replacement.
"This week has been amazing," Townsend said.
In the night session, third-seeded defending champion Jessica Pegula faces Peyton Stearns in another all-American matchup, and No.14 Diana Shnaider of Russia plays No. 6 seed Liudmila Samsonova of Russia.
