Stephens outlasted fellow American Peyton Stearns 6-7 (4), 6-3, 7-6 (6) in 2 hours and 46 minutes. Stephens overcame five double faults and saved 7 of 13 break points. She converted just 28 percent of her second serves.
Trevisan was forced to retire in the second set with an injury. The Italian was down a set to Austrian Julia Grabher, who advances to the semifinals.
In the other quarters, Italian Lucia Bronzetti defeated No. 4 Alycia Parks in straight sets and Julia Riera of Argentina rallied to beat sixth-seeded Yulia Putintseva of Kazakhstan, 5-7, 6-4, 6-2.
Internationaux de Strasbourg
Frenchwoman Clara Burel upended No. 4 seed Bernarda Pera 6-2, 3-6, 6-4 in the quarterfinals in France.
Burel had five aces and saved 11 of 16 break points to advance to the semifinals, where she'll play Elina Svitolina of Ukraine, a 6-3, 6-4 winner over No. 6 Varvara Gracheva of Russia.
Seventh-seeded Lauren Davis rallied to defeat Russian Anastasia Pavlyuchenkova 1-6, 7-6 (2), 6-0 in 2 hours, 34 minutes. Davis will play Anna Blinkova in the semis; the Russian ousted American Emma Navarro 6-4, 6-4.
