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The former champion defeated Elina Svitolina 6-3 6-2 in the quarterfinals.
After almost three hours of nerve-jangling drama, Svitolina gave her war-ravaged homeland something to cheer about when she pulled off the biggest upset of this year's championships.
The American defeated Ukraine's Lesia Tsurenko 6-1, 6-3 in the fourth round.
Venus, 43, has won the third major of the year five times and returned to action this month after a five-month injury layoff.
Svitolina had initially refused to play her opening match against Potapova at the Monterrey Open but went ahead after tennis authorities decided to ban Russian and Belarusian players from competing under the name and flag of their countries.
Ukrainian women's tennis players including Marta Kostyuk and Lesia Tsurenko called on the WTA to pull all tournaments from Russia following the invasion of Ukraine.
The world No. 15 told Eurosport her family and friends in Ukraine were defending the country and that she wanted to help.
Svitolina was aged 21 and ranked 20th in the world when she ousted American great Serena in the third round of the women's singles in Rio but she failed to build on her landmark win by falling in the quarterfinals to Czech Petra Kvitova.
The atmosphere was different for the sixth day of play Saturday at the Australian Open, with no fans to cheer.
She is the first player to go through the season-ending tournament undefeated since Serena Williams in 2013.
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