They will face either 16th-seeded Colombian duo Juan Sebastian Cabal and Robert Farah or Ryan Harrison of the United States and Michael Venus of New Zealand.
A rasping Pliskova forehand gave her a battling hold and she warmed to the task in the second set, causing Halep far more problems with brutal groundstrokes and a venomous serve as she broke for the first time to take a 4-2 lead.
All told, Pliskova committed 55 unforced errors before Halep served out to win the match. Bacsinszky pounced as Ostapenko's radar misfired to break for 4-3 in the second set before the Latvian gifted it to her with a double fault on set point.
The only real sign of nerves came at 3-3 in the second set, when she dropped serve from 40-0 and Bacsinszky went on to level the match.
Suddenly, Halep had to defend, something she does with poise and grace, but Pliskova had recovered her forehand and it made all the difference as she cracked a victor to seal the second set. Halep has played back-to-back three set matches and seems to have gotten stronger in both of the final sets, which is a positive sign considering she has a long history of letting frustration takeover matches.
Ostapenko presented herself with the flawless 20th birthday gift by reaching a first French Open final after blasting past 30th seed Bacsinszky, a semi-finalist also in 2015. I'm really happy to be through to my second semi-final here.
"Still, I think I'm able to play better tennis", Pliskova said, "which, probably, I'm going to need" against Halep.
After her historic win, Ostapenko heard a birthday song from the crowd on the Philippe-Chatrier Court.
"In the third set I just wanted to stay playing aggressive. That helped me win today".
The now retired Ivanovic was present at Roland Garros on Thursday and was honored by the French tennis federation in a ceremony after the first semifinal.
On the day she turned 20 the free-swinging world number 47 launched a fusillade of 50 winners to become the first unseeded player to reach the women's singles final at Roland Garros since Mima Jausovec lost to Chris Evert in 1983.
But her impressive tally of 50 winners, including a bludgeoning forehand on her second match point, helped her become the youngest finalist at any major since Caroline Wozniacki in NY eight years ago.
Also semi-finals in Wimbledon.
None of it worked well enough to win, although here is precisely how close the match was: Ostapenko won 106 points, Bacsinszky 105.
Among them is Jelena Ostapenko of Latvia, now the world's No. 47, whom Pierce said is "definitely someone to watch".