Amanda Anisimova celebrates after winning against Simona Halep at the end of their women's singles quarter-final match. AFP
The 17-year-old downed Halep 6-2, 6-4 on Court Philippe Chatrier to announce herself on the big stage, while Barty saw off 14th seed Madison Keys 6-3, 7-5 to also become a first-time Grand Slam semi-finalist.
"If I didn't look nervous is because I wasn't," said world number 51 Anisimova, who is the youngest player to reach a major semi-final since Nicole Vaidisova at the 2007 Australian Open.
"I was just super excited and I was really happy with the opportunity. "This is more than I could have asked for."
Amanda Anisimova and Simona Halep shake hands after their quarterfinal match. Reuters
The last-four ties will be played on Friday, after Wednesday's downpour in Paris caused a backlog of matches, with the women's semi-finals held on Court Suzanne Lenglen and Simonne Mathieu to keep Chatrier free for the men's semis.
"Actually, I'm really happy that I get to play tomorrow," said Anisimova.
"I don't have to wait a whole day, because I get really eager to want to go on the court, so I'm happy I get to play tomorrow."
She is the youngest American woman to make the last four at a major since Venus Williams at the 1997 US Open, and the youngest to reach the semis at Roland Garros since Jennifer Capriati in 1990.
The defeat for third seed Halep means it has now been 12 years since the last successful title defence in Paris -- Belgian Justine Henin's third straight triumph in 2007.
Still only five women have lifted back-to-back French Open titles in the Open era.
"I feel sad, because every time when I lose, I'm sad," said Halep. "And I'm a little bit upset because I couldn't make my game. I couldn't move normally."
The winner of Anisimova's clash against Barty will face either Britain's Johanna Konta or Czech 19-year-old Marketa Vondrousova in the final.
It is the first time two teenagers have reached the semi-finals at a Grand Slam for 10 years, while it had not happened at Roland Garros since Henin and Kim Clijsters in 2001.
Anisimova crushed 25 winners past a bewildered Halep, who made 17 unforced errors and served two double faults.
Halep's run of breaking in 16 consecutive return games was swiftly ended by Anisimova's big hitting, and the American broke serve in fifth game en route to a 4-2 lead.
She saved a break point and then dismantled the Halep serve once more to seal the opening set in under half an hour.
Halep, who had thrashed 18-year-old Pole Iga Swiatek 6-1, 6-0 in the fourth round, faced being on the wrong end of a similarly one-sided match when she fell 3-0 down in the second.
Anisimova tightened up with the semis in sight and the defending champion fought back to 4-4, but the youngster gathered herself to save a break point in the next game and then grabbed her first match point with a glorious backhand winner up the line.
Barty sees off Keys
Barty also won in relative comfort on Court Suzanne Lenglen to go one better than her run to the Australian Open last eight earlier this year.
The 23-year-old was too consistent for American Keys, hitting 16 winners and four aces.
Keys, a semi-finalist at Roland Garros last year where she lost to Sloane Stephens, was undone by 26 unforced errors.
World number eight Barty is the highest-ranked woman in the semi-finals, ahead of 26th seed Konta and the unseeded youngsters Anisimova and Vondrousova.
But she insisted it would not give her an advantage, saying: "As I just said, all four of us have been playing great tennis. It's a new situation for me. It's a little bit of a new territory."
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