Brengle showed poise to save a set point and break the teenager as she served for the set, but Anisimova was unmoved, breaking back in the next game to claim the set.
Dropping serve for a second straight time, the French Open semifinalist shook off the early deficit to win six of the final seven games, securing victory on her second match point.
In all, she struck an even 18 winners to 19 unforced errors while converting eight of 12 break point opportunities to edge into the last eight in under an hour, where the American will next face China’s Zheng Saisai, who upset No.8 seed and 2018 San Jose semifinalist Danielle Collins earlier in the day.