America's Anisimova dazzled in a crushing 6-2 6-4 win over third seed Halep, who was looking to become the first woman to retain the title since Justine Henin's three consecutive triumphs from 2005-07.
Instead, 17-year-old Anisimova will take on Ashleigh Barty in the last four after the Australian beat another American Madison Keys 6-3 7-5.
The other semi-final will pitch teenager Marketa Vondrousova against Briton Johanna Konta, meaning it is the first time since the 1978 Australian Open that none of the last four women at a major have reached a Grand Slam final before.
Saturday's winner will be the ninth different Grand Slam champion in the last 10 majors and a teenager could lift the trophy at Roland Garros for the first time since Iva Majoli in 1997.
Beating the defending champion on centre court was no small feat for Anisimova, but the unseeded American was nerveless throughout.
"I didn't look nervous because I wasn't. I was just super excited, and I was really happy with the opportunity," she told reporters.
The wild unpredictability of the women's tournament is in sharp contrast to the men's event, which will feature Rafael Nadal, Roger Federer and Djokovic together in the last four for the fifth time since 2007.
After Wednesday's action was a complete washout, Thursday's matches were all won in straight sets as world number one Djokovic dismissed German fifth seed Alexander Zverev 7-5 6-2 6-2.
He will meet Austrian fourth seed Dominic Thiem, who beat Russian Karen Khachanov 6-2 6-4 6-2, with the other semi-final pitching Federer against Nadal in the 39th instalment of their rivalry.
Top seed Djokovic was in ominous form as he continued his bid to hold all four Grand Slam titles for the second time in his career.
Thiem is also becoming part of the furniture at Roland Garros as the Austrian reached the last four in Paris for the fourth consecutive year.
The men's semi-finals will be played on Court Philippe Chatrier with the women's relocated to Court Suzanne Lenglen and Court Simonne Mathieu after Wednesday's washout caused them to be delayed by one day.
(Reporting by Julien Pretot; Editing by Toby Davis)
