Haddad Maia, who reached the fourth round of the U.S. Open, breezed through the first set in 36 minutes and took a 5-1 lead in the second set. But the 31-year-old Pigossi proved to be a tough out, holding serve twice and breaking the highest-ranked Brazilian woman in the eighth game.
She won two of the first three points in the 10th game, but Haddad Maia won the final three points and captured the second-round match.
Haddad Maia on Friday will take on fifth-seeded Mexican Renata Zarazua, who bested Turkey's Berfu Cengiz 6-4, 6-4. Zarazua defeated Madison Keys in the first round of the US Open.
Hungary's Panna Udvardy defeated another home-country favourite, Ana Candiotto, 6-3, 6-3.
Follow all the action in Sao Paulo here.
Mertens and Kudermetova fall in Guadalajara
The two top seeds, Belgium's Elise Mertens and Russia's Veronika Kudermetova, fell in the afternoon session during second-round play in Guadalajara, Mexico.
The top-seeded Mertens dropped a 4-6, 6-3, 6-4 decision to France's Elsa Jacquemot in a two-hour, 31-minute thriller, while Andorra's Victoria Jimenez Kasintseva vanquished second seed Kudermetova 6-4, 6-2.
Mertens was broken at 15-40 in the first game of the deciding set and lost her serve at love in the fifth game. Jimenez Kasintseva fended off all four of her opponent's break point chances, while capitalising on 3 of 6.
In the other afternoon match, Colombia's Emiliana Arango defeated Australian Storm Hunter 6-2, 6-2.
Third seed Jelena Ostapenko of Latvia, the top seed remaining, was scheduled to face Canada's Marina Stakusic in the evening session, but the match was moved to Friday.