Anisimova, into her first Masters semi-final, advanced to a Sunday showdown against US eighth seed Emma Navarro, who eliminated fellow American lucky loser Taylor Townsend 6-3, 7-6 (7/5).
Anisimova, 22, will try to reach her fourth career WTA final and first since winning at Melbourne in January 2022.
She also won at Bogota in 2019 after losing her first career WTA final at the 2018 Japan Open.
World number 15 Navarro, 23, won her only prior WTA final in January at Hobart.
World number three Sabalenka was broken in the 10th game to drop the first set, netting a backhand to surrender to set then slamming her racquet to the court in frustration.
After an early exchange of breaks in the second set, Sabalenka netted a backhand to give 132nd-ranked Anisimova a break and a 4-2 edge.
Anisimova, who has not lost a set this week, then won the last eight points -- holding at love for a 5-2 lead and breaking at love to complete the upset after 86 minutes when Sabalenka double faulted.
Third-seeded defending champion Jessica Pegula was set to face fellow American Peyton Stearns in a later quarter-final.
Russia's Diana Shnaider, who ousted US top seed and reigning US Open champion Coco Gauff on Friday, also had a later quarter-final -- against Russian sixth seed Liudmila Samsonova.
Shnaider, ranked 24th, seeks her fourth WTA title of the year after Thailand, Bad Homburg and Budapest.
