Suarez Navarro started the day by beating Shuai Peng 6-3 7-6 (7-4) and Llagostera Vives, followed with a 6-3 6-4 win over Jie Zheng.
"I played a great last two games," Llagostera admitted, "but it would not be the first time a team has been 2-0 down and has won three points on the second day so we have to be focused (Sunday)."
A nation has bounced back from a 2-0 first-day deficit just three times since the international women's tennis competition started in 1963.
The Spain-China winner faces either Russia or the United States in the final in September.
Russia holds a similar 2-0 lead in Moscow.