The 14th seed received plenty of vocal support from the stands as she emulated the 1978 and 1979 feat of Patricia Medrado.
"There are many Brazilians here, I am very happy and grateful for the support, it is very special to be able to represent you all," Haddad Maia said.
She broke into the Top 20 last year after winning back-to-back titles on grass in Nottingham and Birmingham, and reaching her first WTA 1000 final in Toronto.
Haddad Maia will face Spain's Sara Sorribes Tormo (26) in the fourth round on Monday.
