"No matter what else happens, this is a great step forward," Kournikova said after beating unseeded Wynne Prakusya.
"A month or two ago I wouldn't have pulled this out," said Kournikova, who was beaten in the first round of her past four tournaments. "This has already been great having won two matches."
"I always play well at Stanford," said Kournikova, who improved to 7-2 in her third tournament at Taube Family Tennis Center. "After practicing in Florida, where it's hot, it feels nice here."
"I have nothing to lose," Kournikova said. "I'm just going to enjoy it and stay on the court as long as I can."