The Belgian, ranked No.17 in the world, prevailed 6-2 4-6 6-4 over Kristina Mladenovic of France in two hours and 40 minutes to advance in San Jose.
She moves on to face the No.8 seed, Yulia Putintseva, who rallied past Ajla Tomljanovic 3-6 7-5 6-3 as the Australian blew numerous chances to pull ahead by converting only two of 16 break-point opportunities.
In the bottom half of the draw, No.2 seed Elena Rybakina remained on track with a 2-6 6-0 6-2 victory over American Claire Liu in a rematch of a second-round meeting at Wimbledon.
Rybakina next meets No.7 seed Danielle Collins, a 3-6 6-4 6-3 winner over US countrywoman Sloane Stephens.
Stephens, the 2017 US Open champion, has slipped to No.67 in the world and was playing in her first tournament since Wimbledon as she prepares for a return to Flushing Meadows.