In the other match, teenager Ostapenko, playing at Roland Garros for just the second time in her career, defeated former world No.1 Denmark's Caroline Wozniackion 4-6, 6-2, 6-2 in one hour and 53 minutes.
The first woman from her country to reach a Grand Slam quarterfinal - beating 2016 Olympic gold medalist Monica Puig and 2010 French Open finalist Samantha Stosur en route - the 47th-ranked Ostapenko has not yet won a title on the WTA circuit.
For now, Ostapenko is the first teenager in the French Open semi-finals since Ana Ivanovic in 2007.
Jelena Ostapenko and Timea Bacsinszky embraced after ensuring they will meet in the semi-finals of the French Open on their birthdays, while tennis legends were rolling back the years on a rainy day in Paris.
"Caroline is a tough opponent, I knew I had to stay aggressive, I lost it sometimes but I found my game".
"Lucky for her that she's just 20 but maybe lucky for me as I have more experience!"
"The one thing we did when Ivan [Lendl, his coach] got here, we went right back to the basics", said Murray yesterday.
Jelena Ostapenko pulls off an exceptional upset at Roland Garros. Then the Dane finished a crucial break in the 10th game to take away the first set 6-4.
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Ostapenko is not looking beyond her clash with Bacsinszky as she revels in an unexpected challenge for the Coupe Suzanne Lenglen. They play Thursday, which happens to be Ostapenko's 20th birthday and Bacsinszky's 28th. "I hope I can enjoy it". "Lucky her, she's way younger than I am!"
Fighting through rain delays, Ostapenko reaches the semifinals at the 2017 French Open. "Because to play semi-final of Roland Garros on your birthday, I think it's really nice", added Ostapenko.
"At the end, it's a quite close scoreboard, 4 and 4, but I feel I'm very far from the game I could have shown". So it was a big drama, so I could not get into the plane without giving the towels of the French Open, and I woke up and I was sweating.
- A hilarious Timea Bacsinszky pretends she's an umpire for a second as she waits for reporters to take their seats for her press conferences. Both players struggled to hold serve but, leading 5-4, Bacsinszky fired down an ace to seal the set against the local favourite.
Mladenovic, bidding to be the first Frenchwoman in the semi-finals since Marion Bartoli in 2011, was broken in her first service game by Bacsinszky before she levelled at 2-2.
The Switzerland native had to fight the blustery conditions and the pro-French crowd cheering on Mladenovic while prevailing on Court Philippe Chatrier.
Both women's quarterfinals were interrupted twice because of showers; the first delay lasted more than 3 hours, the second about a half-hour.