Nadal broke Lorenzi's serve five times and lost only five points on his serve, never facing a break point.
Nadal's opponent in the quarterfinals will be Yoshihito Nishioka of Japan, who eliminated Aussie Jordan Thompson 6-4, 3-6, 6-0. Nishioka defeated seventh-seeded Jack Sock in three sets in the first round.
Top-seeded Novak Djokovic faced a strong challenge from Argentina's Juan Martin del Potro on Wednesday, but the Serb emerged with a 4-6, 6-4, 6-4 victory.
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Next up for Djokovic is a quarterfinal matchup with sixth-seeded Nick Kyrgios of Australia, who defeated Donald Young of the United States 6-2, 6-4.
"I played really well today," Kyrgios said. "I'm really enjoying my time here."
American Sam Querrey recorded the biggest upset of the day, eliminating fifth-seeded David Goffin of Belgium 6-2, 6-3 in 69 minutes. Querrey lost only four points on his first serve.
Third-seeded Marin Cilic of Croatia was pushed to three sets but won the critical points to beat 20-year-old Borna Coric of Croatia 6-3, 2-6, 6-3. Cilic, who fired 12 aces, had only two break-point opportunities in the third set but converted both to improve his record against his countryman to 4-0.
Cilic's quarterfinal opponent will be American Steve Johnson, who eliminated Ernesto Escobedo 7-6 (5), 6-3.
Fourth-seeded Dominic Thiem of Austria scored a 7-5, 6-3 win over France's Adrian Mannarino.
