British number one Emma Raducanu was beaten in the third round at Indian Wells by Croatia's Petra Martic but qualifier Harriet Dart went through by defeating Estonia's Kaia Kanepi.
Dart, 25, won 7-6 6-3 and her run in this event could see her break into the world's top 100 for the first time.
"My ranking might not show where my level is, but I've always believed my level has been there," the Briton said.
"I put in the work day in, day out, and finally to be able to put a run like this together, it's not by chance.