The top-seeded Nadal recorded a 6-3, 6-1 victory over Italy's Fabio Fognini, while the second-seeded Federer registered a 6-4, 6-2 triumph over Ukrainian qualifier Alexandr Dolgopolov.
Nadal's victory took just 63 minutes and extended his winning streak to 14 consecutive matches.
"Of course, it's good news, and especially in this part of the season," Nadal said. "It's better like this than having long matches. You save a little bit more the body.
"It doesn't matter how long you are on court, (the) most important thing is be enough competitive to (handle) all the situations."
The Spaniard is 63-9 this season and has won six titles. His quarterfinal opponent will be sixth-seeded Grigor Dimitrov of Bulgaria, who posted a 6-3, 7-6 (3) victory over 10th-seeded American Sam Querrey.
"I'm going to have a tough match against Grigor," Nadal said. "I know I have to play my best if I want to keep having chances of success. I hope to be ready to do it, because I am playing well."
Federer also was hardly challenged in his victory over Dolgopolov. The Swiss star delivered 11 aces and won 80.4 percent of his service points.
Dolgopolov won two of the four games of the second set before Federer turned it up a gear and have won the final four games.
"I like playing Gasquet on fast courts," Federer said afterward. "I hope I can again put on a similar performance like today."
The 16th-seeded del Potro recovered from losing the first set to knock off Zverev for the first time.
Zverev, 20, had an in-match meltdown when he lost the fifth game of the final set after having a 40-15 lead. Zverev smashed his racket until it was broken.
"For me, it's impossible to lose a match when I've only been broken one time," Zverev said. "The game where he broke me, I was up 40-15, and I was just unfocused there."
Del Potro felt the sequence put him in complete control.
"I saw his frustration, for sure," del Potro said. "He's still very young and has to keep learning. He has everything to be in the top of the game."
Del Potro will face Serbian Viktor Troicki in the quarterfinals. Troicki knocked off 12th-seeded American John Isner 6-4, 7-6 (4) to advance.