Defending champion Nadal, chasing a 10th title at the tournament, will face either Argentina's Diego Schwartzman or German qualifier Jan-Lennard Struff for a place in the semi-finals.
Earlier, world number one Andy Murray, world number three Tomas Berdych and and world number 12 Stan Wawrinka were all eliminated from the last 16 of the tournament.
Murray suffered a shock defeat to Spain's 15th seed Albert Ramos-Vinolas, losing 2-6, 6-2, 7-5 in more than two and a half hours.
Former French Open champion Stan Wawrinka was also routed, with the Swiss third seed losing to Pablo Cuevas of Uruguay 6-4, 6-4.
Ramos-Vinolas will face Marin Cilic in the quarter-finals on Friday after the Croatian's 6-2, 7-6 (7/0) win over Berdych.