Halep carved out a break for 3-1 in the decider, an inch-perfect pass proving fair reward for her stalwart defence.
In Saturday's championship match, the 47th-ranked Ostapenko will face Simona Halep of Romania, who got past 2016 U.S. Open runner-up Karolina Pliskova of the Czech Republic 6-4, 3-6, 6-3 in the second compelling semifinal on a sunny day with the temperature touching 81 degrees (27 Celsius).
The Latvian turned 20 on Thursday and Marion Bartoli led the Court Philippe Chatrier crowd in singing "Happy Birthday", in French, to Ostapenko moments after her victory.
"But then, like, first match was a tough match, as well, and I won it. I think it's a nice gift", she said.
Here are a few fun facts about Ostapenko.
The contest was tight, Ostapenko winning 106 points to Bacsinszky's 105, but even that did not spoil the mood of the Swiss, who was obviously disappointed but dejected. It was measured at 76 miles per hour (122 kph), faster than the average of top-ranked men's player Andy Murray.
Jausovec eventually lost to Chris Evert of the United States 6-1, 6-2. "Normally, my backhand is my favorite shot", Ostapenko said with a smile. "It actually makes me cry now".
She has 245 winners from six rounds - more than Andy Murray s 174 after five matches. Her successful all-or-nothing approach saw her fire 50 winners and 45 unforced errors against Bacsinszky.
"She came out like a thunderstorm in the third set".
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And Patty, as you know if you've met her, is so intense and passionate and clear and decisive and a master storyteller. Pictures and DC Films' Wonder Woman has earned $11 million in Thursday previews with $1.5 million from IMAX.
She has a total lack of fear.
The Latvian is also eight centimetres taller, meaning it was easier for Ostapenko to hit the ball harder. It's a habit that players tend to grow out of, when the importance of winning changes, but for now she goes for broke. She doesn't measure maybe what she's doing right now.
"The best example is the match point".
But overcoming Halep could prove to be very hard. "I would be surprised if she came out and hit winners all over the court like she has been doing". It comes that [high] above the net and in the corner. "I had no idea what does it mean". But she does it. She found herself trying to fight her way out of error after error throughout the match.
"We were a bit unsure how she would be after the ankle injury (at the Italian Open) in Rome but she seems to be getting better and better with every match", she added. She is the first unseeded player to reach the women's singles final here since 1983.
A three-time champion at Roland Garros, Kuerten will be honored before Sunday's final when he will receive his Hall of Fame ring during a ceremony marking 20 years since he won his first title in Paris.
If she wins, she'll be one of the biggest outsiders ever to take the title.