"I'm happy because Roberto is a very good player. It's very important for me to be in the quarter-finals one more time," said Nadal, who turned 31 on Saturday.
"Probably I didn't play as well as I did the other day, but I still played well."
The fourth seed will meet compatriot Pablo Carreno Busta, through to his first Slam quarter-final, for spot in the last four after the latter stunned Canada's Milos Raonic.
Carreno Busta, seeded 20th, needed seven match points to clinch a thrilling 4-6, 7-6 (7/2), 6-7 (6/8), 6-4, 8-6 win over the fifth-seeded Raonic.
Djokovic also became an 11-time quarter-finalist as he sauntered past Spain's Albert Ramos-Vinolas 7-6 (7/5), 6-1, 6-3.
The Serb needed 75 minutes to clinch the opening set but then outclassed the 19th seed to set up a showdown with Dominic Thiem.
"There's no easy match in a Grand Slam quarter-final, it will be very difficult for both of us," said Djokovic of his upcoming challenge.
The Serb also confirmed that coach Andre Agassi had, as planned, already left Paris.
Austrian sixth seed Thiem thrashed Argentina's Horacio Zeballos 6-1, 6-3, 6-1 to reach the quarters for a second straight year.
Japan's Kei Nishikori fought off a fierce challenge from South Korea's Hyeon Chung in an all-Asian tussle held over from Saturday following rain to clinch a place in the last 16.
Chung quickly forced the contest into a fifth set as play resumed on Sunday, but the world number 67 double faulted on match point to gift Nishikori a 7-5, 6-4, 6-7 (4/7), 0-6, 6-4 victory.
"I think the rain helps me a lot, because I was really down in the fourth set and mentally I wasn't ready," admitted Nishikori, who faces Fernando Verdasco next.
Karen Khachanov will play Andy Murray in the fourth round after the giant Russian beat American 21st seed John Isner 7-6 (7/1), 6-3, 6-7 (5/7), 7-6 (7/3). Kristina Mladenovic ensured the host nation will have two women in the quarter-finals for the first time since 1994 after dumping out fourth seed Muguruza 6-1, 3-6, 6-3.
"I'm sad. It's a very painful defeat here in the French Open," said Muguruza, who left Court Suzanne Lenglen angrily wagging her finger at the crowd. "I just think that they sometimes should be a little bit more respectful," she added, as Mladenovic thrived on the partisan support.
The French 13th seed is through to just her second Slam quarter-final -- after the 2015 US Open -- and will face Switzerland's Timea Bacsinszky for a spot in the last four. The Swiss 30th seed, a 2015 semi-finalist, defeated 2002 runner-up Venus Williams 5-7, 6-2, 6-1 to guarantee a first-time major champion will be crowned next Saturday. .AFP