Playing on the Suzanne Lenglen court, Bia closed the game in 2 sets to 1, with scores of 6-7 (3/7), 6-3 and 7-5.
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The Brazilian will compete for a place in the semifinals with Tunisian Ons Jabeur, number 7 in the world, who easily beat American Bernarda Pera (36th), with scores of 6-3 and 6-1, in just over an hour.
Bia and Sorribes played one of the best games of the tournament, the longest of the year on the women's circuit, in which the Brazilian's offensive repertoire overlapped with the Spaniard's backcourt play.
Sorribes, who had never gone beyond the third round of a Grand Slam, showed that she is fully recovered after suffering a fracture in her right foot, which kept her out of action from September last year to April this year.
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Bia, who is enjoying the best phase of her career at the age of 27, became the first Brazilian to reach the quarterfinals of Roland Garros since Maria Esther Bueno, in 1968.
The tennis player from São Paulo was the favorite and seemed to be on her way to a quiet victory when she took a 5-2 lead in the first set, but Sorribes reacted with three breaks and forced a tie break, which she won 7/3.
The Spaniard kept the pace and took a 3-0 lead in the second set, but this time it was Bia who reacted and won six games in a row to tie the match.
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In the decisive set, with both already fighting fatigue, Bia served to close the match in the 12th game and sealed the victory on her fourth match point.
