Halep, the 2014 runner-up, was down 5-1 in the second set, then was a point from losing while down 6-5 in the tiebreaker but came up with a backhand victor down the line to extend the match.
However, Ostapenko never wavered from her all-or-nothing approach and she regained her hot streak in the last three games to become the first unseeded woman to reach the final since 1983.
The Latvian powered her way to a 7-6 (7/4) 3-6 6-3 victory to become as the youngest player to reach a grand slam final since Caroline Wozniacki in NY eight years ago.
For 30th-seeded Bacsinszky it was a second semi-final defeat in three years in Paris. I have the mentality to win, but it's gonna be tough. At 6-1, Ostapenko is the long shot of the four players remaining.
"It's an incredible feeling right now", said Halep after her fifth win in six meetings against Pliskova.
"That's how it is and I think it's a good fight for world number one".
Pliskova then broke to level the set but Halep broke straight back to leave the Romanian serving for the match.
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"And now it's close, but it's close and it's far because I'm playing against somebody who I would say one of the best girls on clay".
Twice she served for victory at 5-2 and 5-4 before going on to waste a match point at 6/5 in the tie-breaker.
The Latvian, who turned 20 on Thursday, is also the youngest woman to advance to the final of a major since a 19-year-old Caroline Wozniacki finished runner-up at the 2009 US Open. "I think it's a nice gift".
Earlier, India's Rohan Bopanna and Canada's Gabriela Dabrowski saved two match points to claim their first Grand Slam title with victory in the French Open mixed doubles final. I'm not ashamed to say that she played better.
For the match, Svitolina struck 36 winners to Halep's 26 but she also committed 18 more unforced errors (45 to 27). Yet she showed remarkable composure after being made to wait for the start of the third set by a Bacsinszky bathroom break, smashing her way into the Roland Garros final.
At the moment, however, all she cares about is hitting the ball hard - very hard - and seeing where it gets her.
She said: "I'm really happy with my win today and it was a really tough match".
Saturday's final will see a new Grand Slam champion crowned, and a new name at the top of the rankings should Halep win and overtake Angelique Kerber.