Olivetti, No. 388 in the world, got past Fish, who is ranked No. 8, 6-3, 3-6, 6-3 by scoring the only break of the third set. He was good on just 49 percent of his first serves and had nine double faults but still had 23 aces.
He'll next face fifth-seeded Richard Gasquet, who on Thursday ran over Igor Kunitsyn 6-3, 6-2. Gasquet fought off six break points while converting three of his four chances.
Michael Llodra outlasted No. 6-seeded Alexandr Dolgopolov 6-4, 5-7, 7-6 (7-5) to earn a quarterfinals slot. Llodra, who won the event two years ago, won four consecutive points in building a 5-2 lead in the tiebreaker.
With Gasquet, Llodra and Olivetti winning Thursday, there will be five French players in the quarterfinals. No. 1-seeded Jo-Wilfried Tsonga and Edouard Roger-Vasselin qualified with wins Wednesday.
Tsonga and Roger-Vasselin are paired against each other in the quarters while Gasquet takes on Del Potro in the other match in that half of the draw. Llodra and Olivetti also meet with third-seeded Janko Tipsarevic and No. 7-seeded Ivan Ljubicic playing in the other match.