The Guernsey-born 20-year-old, ranked a career-high 79th in the world after an impressive run at Wimbledon, will now meet Yanina Wickmayer for a place in the quarter-finals of the Bank of the West Classic.
World number 37 Wickmayer was also taken to three sets, eventually edging Kai-Chen Chang of Chinese Taipei 7-5 2-6 7-5 to book her place in the second round. The Belgian reached the last eight at Stanford two years ago.
Also progressing into the next round were Chanelle Scheepers of South Africa and Portugal's Michelle Larcher de Brito.
Scheepers, seeded sixth, beat Grace Min of the US 6-4 6-4, while Larcher de Brito saw off Australia's Jarmila Gajdosova 5-7 6-2 6-3.
And finally, Coco Vandeweghe of the US beat Hungary's Melinda Czink 6-4 6-1 to set up a meeting with Jelena Jankovic.
Wimbledon champion Serena Williams headlines the draw, while Britain's Anne Keothavong also features.