Ostapenko and Bacsinszky are set to meet for a place in the final on Thursday - which will be a birthday for both players.
The world number 47 has produced some of her finest performances on clay this season including a runner-up finish in Charleston before reaching the final four in Prague.
Her 4-6, 6-2, 6-2 win over Caroline Wozniacki on Tuesday marked the third time she won a match at this French Open after losing the first set.
Ostapenko is just the fourth of those at Roland Garros following Clarisa Fernández in 2002, Nadia Petrova in 2003 and Kiki Bertens in 2016.
And sure enough Mladenovic - who trailed Jennifer Brady 3-0 in the third set in the first round and a second American, Shelby Rogers, 5-2 in the third set in the third round - temporarily lifted her game to lead 3-1 in the second.
"I'm really happy, I love to be here", Ostapenko said after the crowd serenaded her with a chorus of "Happy Birthday" on the day of her 20th birthday.
Bacsinszky, the 30th seed, who needed a bandage applied to her right thigh midway through the first set, looked the more likely victor at that point as she sought to celebrate her 28th birthday by surpassing her semi-final run of 2015.
She took it when the Frenchwoman fired a forehand volley wide.
It seemed like Mother Nature was doing her utmost to help Kristina Mladenovic at the French Open Tuesday but she just couldn't take advantage.
Ferrari dominates final practice with Vettel, Raikkonen one-two; Stroll 18th
Nico Hulkenberg , the Force India's and Felipe Massa were also in a risky spot as they could easily fall out of the top ten. In Q1, Bottas was first into the 1:12s in qualifying with his best lap of the weekend to date in his Mercedes at a 1:12.864.
Unseeded women are 4-15 in the French Open semifinal in the open era.
"In my mind, every time I go on court to play against her, I just know that I have to stay aggressive, but to not go for every shot because I have to be consistent, as well".
Ostapenko (19) had struggled against the wind during the opening set on Suzanne-Lenglen, which Wozniacki took control of with two early breaks of serve to race into a 5-0 lead.
The winners were flying off of Ostapenko's racket on almost every point, Wozniacki with no answer to her opponent's sensational performance. The Latvian player wrapped up the set in 31 minutes.
Here are the pairings for the men's and women's semifinal matches and TV times.
It is the first major since the 1979 Australian Open where no women's quarterfinalist was a Grand Slam champion.
"I hope I can play better than the previous time and that the score will be different", said Halep, who lost in three sets to Maria Sharapova on her first appearance in the final at Roland Garros.
The other semifinal match will pit top-ranked Andy Murray against 2015 champion Stan Wawrinka.
Caroline Garcia, Karolina Pliskova, Elina Svitolina and Simona Halep will contest the bottom half quarter-finals tonight.
"We played doubles together in Wuhan a year ago and we have practised a lot together".
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