Pierce, the second-seed from France, made short work of Slovakia's Karina Habsudova, 6-2, 6-4, in a match which was cancelled on Wednesday due to rain.
An hour later, she stepped back on the court and battled the with the elements before beating Argentina's Florencia Labat 7-5, 6-3.
"I feel like I'm in good form. Two matches on one day are no problem," said Pierce, the Australian Open winner.
The top seed, Spain's Arantxa Sanchez Vicario, had no trouble beating Tatiana Ignatieva, of Belarus, 6-2, 6-1, but Gabriela Sabatini, the fourth seed from Argentina, showed her inconsistency again, being beaten 7-6, 6-4 by Australia's Nicole Bradtke.Reuse content