Play was held up for over three hours yesterday before finally resuming at 1845 local time (1645 GMT) with the first two women's quarter-finals at Roland Garros.
"Lucky her, she's way younger than I am", said Bacsinszky, the No. 30 seed from Switzerland who defeated France's 13th-seeded Kristina Mladenovic 6-4, 6-4 on Tuesday in a quarterfinal match twice delayed by persistent rain and stormy weather for a total of nearly four hours.
Asked what her best birthday present has been so far, she said: "I think maybe this one is one of the best ones". "So I think if I keep it up, I think anything can happen".
Ostapenko had never been beyond the second round of a grand slam before the Australian Open this year, but can now look forward to the biggest match of her life on her first day in the 20s after becoming the first Latvian woman to reach the semi-finals of a major in the Open Era.
Bacsinszky and Ostapenko are set to meet on Thursday - which will be both players' birthday - with a place in the final at stake.
The 27-year-old Bacsinszky on Tuesday defeated Frenchwoman Kristina Mladenovic 6-4, 6-4 in one hour and 49 minutes in a quarter final match, reports Efe.
An empowered Bacsinszky broke again at love-her third straight game-to go back up a break, 4-3.
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"I knew", the 47th-ranked Ostapenko said, "I had to be aggressive all match".
Ostapenko, 19, had struggled against the wind during the opening set on Suzanne-Lenglen, which Wozniacki took control of with two early brakes to race into a 5-0 lead.
She will play Swiss 30th seed Timea Bacsinszky, who beat France's Kristina Mladenovic 6-4 6-4.
Djokovic's progress has been troublesome in comparison, being stretched to five sets by Diego Schwartzman in round three - but the battle-hardened Serb is well-versed in the business end of slams and usually raises his game.
China's Zhang Shuai bid farewell to the 2017 French Open after losing to the eighth-seeded Svetlana Kuznetsova 7-6 (5), 4-6, 7-5 in the women's singles third round, while men's defending champion Novak Djokovic had to endure a five-set thriller to see off Diego Schwartzman here on Friday. She's had great results here in the past.
The second-seeded Czech fended off three break points on her way to claiming the second set 6-3, clinching it with a forehand victor on her second set point. I was just doing some, like, Latin championships in ballroom dancing. I saw her in the gym just right after our matches today, and so we both said, like, mutually to each other, "Well done". I was happy for her that she was in the semi-final, as well. After a backhand attack went out, Zhang stopped her quest for a last 16 berth in the tournament.
A resurgent Rafael Nadal has been the top performer on the dirt and the nine-time French Open champion will be expected to get past fellow Spaniard Pablo Carreno Busta in his quarterfinal.
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