Thiem's next opponent will be Nadal, as the "King of Clay" was on his run for the 10th success at Roland Garros.
Nadal met little resistence from his Spanish compatriot Pablo Carreno Busta in their 51-minute matchup, as the 20th-seeded Busta retired when Nadal was leading 6-2, 2-0.
In the women's field, due to an early exit from world No. 1 Angelique Kerber, Halep and the second-seeded Karolina Pliskova were involved in a tense battle for the top position on WTA rankings.
Halep once faced the threat of an elimination after she lost the opening set 6-3 and was 5-1 down in the second, before bouncing back strongly into the match as she won five games in a row to turn around the tables.
After winning the thrilling tiebreak 8-6, she continued her in-form display to finish a bagel in the decider.
Halep booked a head-to-head semifinal contest with Pliskova, who got past local favorite Caroline Garcia 7-6 (3), 6-4.
The other semifinal of women's singles will be played between 30th seed Timea Bacsinszky and underdog Jelena Ostapenko of Latvia.
China's Zheng Saisai found it difficult to play at her best level due to a knee injury, as she and her Romanian partner Irina-Camelia Begu lost to Australian duo of Ashleigh Barty and Casey Dellacqua 6-3, 6-4 in the doubles quarter-finals.
The 15-year-old Chinese youngster Wang Xinyu also crashed out from the tournament with a 6-3, 4-6, 6-4 loss to Whitney Osuigwe in the girls' singles third round.
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