Now she stands one match away from becoming the first unseeded player in the professional era to win the women's title at the French Open and the first Latvian grand slam champion.
Halep drew first blood in the final set when she connected on a running forehand victor to break for 3-1.
Should Ostapenko, who had never won a match at the French Open before last week, beat Halep she would become only the second unseeded player to win the women's title after Great Britain's Margaret Scriven achieved the feat in 1933.
"I really happy, I love to play here and I'm just happy the way I celebrate my birthday", Ostapenko grinned.
"I hope this time I can play better", Halep said, "and I can win it".
"I'm already in the final." she said.
Bacsinszky - whose birthday was also Thursday; she turned 28 - employed all manner of strategies in a bid to throw off her opponent.
Twice a finalist on hard courts, Ostapenko arrived here proving that her aggressive game worked just as well on clay: a semi-finalist in Prague and runner-up in Charleston, and here she had beaten Sam Stosur and then Wozniacki, both from a set down, to stack up more hours on court than any of the four semi-finalists.
For Halep, the win came just a day after she saved a match point and came from a set and 1-5 to beat Elina Svitolina in the last eight.
"I think today I showed that I'm stronger mentally", Halep was quoted as saying on the French Open's official Web site.
Czech second seed Pliskova would have become world number one next week had she won the second semi-final. "It keeps us hanging on our seats with every match and we get surprises along the way, and fantastic tennis as well", said Pierce, who is the WTA Finals ambassador.
"I don't think we can ever see another guy like this", Kuerten said. She's one match from it and hardly seems flustered by the possibility.
Pliskova tallied 33 winners and 31 unforced errors in the final two sets, so it was the first set that cost her.
Pliskova ended the tie with 45 winners and a staggering 55 unforced errors. Pliskova had a resilient match, battling back from deficits throughout, but Halep ultimately proved to be too much, taking the match 6-4 3-6 6-3.
Ostapenko, ranked 47 in the world, will now play Romania's Simona Halep in the final. I won the first set and was very close to making the final and some thoughts were in my mind. She was braver. She had more courage.
The Czech said: "Ostapenko is having a good run here, and she's a unsafe player for everybody, but I would bet everything what I have on Simona".
Didn't really show. She surged in the tiebreaker, winning four of the last five points and ending it with a swinging backhand volley victor.