Clijsters has been slowed this spring by injuries and was defeated in the second round of the French Open. She struggled to a first-round win at the UNICEF Open but Oprandi, No. 82 in the world, pulled off a 7-6 (7-5), 6-3 upset.
Oprandi dropped serve only once and fought off all three of the break points she faced in the second set.
Kimiko Date-Krumm also earned a quarterfinal slot Tuesday, defeating Lourdes Dominguez-Lino 7-6 (7-3), 6-0. After the tight first set, Date-Krumm won 70 percent of the points in the second.
Seventh-seeded Roberta Vinci was a first-round winner Tuesday with a 6-4, 6-2 victory over Polona Hercog.
Also in the first round, Jelena Dokic beat Alla Kudryavtseva 6-0, 6-4; Johanna Larsson edged Rebecca Marino 7-5, 7-5; and Sara Errani eliminated Kiki Bertens 7-6 (8-6), 6-1.