Djokovic, the 2013 Monte Carlo winner and a two-time runner-up, needed just 56 minutes in a 6-4, 6-0 rout of Austria's Andreas Haider-Maurer, while Nadal had a little more difficulty disposing of John Isner. The eight-time Monte Carlo champ moved on with a 7-6 (8-6), 4-6, 6-3 triumph over the towering American.
Nadal won this clay court title eight straight years from 2005-12, beating Djokovic in the 2009 and 2012 finals. Djokovic ended the Spaniard's run with a surprising victory in the 2013 title match.
Next up for the top-seeded Djokovic will be Marin Cilic in the quarterfinals. The eighth-seeded Croat topped Frenchman Jo-Wilfried Tsonga, 6-3, 7-6 (7-5), on Thursday. Cilic has never beaten Djokovic in 11 all-time meetings.
The surprises at the bottom of the draw occurred early on Thursday, as Gael Monfils knocked off the second-seeded Federer, 6-4, 7-6 (7-5), while Grigor Dimitrov made quick work of the seventh-seeded Wawrinka, 6-1, 6-2.
Monfils rallied from a break-point down in the first set, breaking Federer's serve a second time in the ninth game before a hold to win it. The Frenchman then won the last four points of the second-set tiebreak after trailing 5-3.
"It was not the best end to the match," said Federer, a four-time runner-up in Monte Carlo. "I should have done better with the break up in the first. I think I did a good job to hang around the second set. I also had chances of my own. It remained close, but I never felt like things were really happening the way I wanted them to be going during the whole match."
Wawrinka, who beat Federer in last year's Monte Carlo final, lost the first four games of his match Thursday and never recovered. Dimitrov saved all six break points he faced and finished off the match in a mere 55 minutes.
Dimitrov, this week's ninth seed, advanced to the quarterfinals in Monte Carlo for the second time. He lost to Rafael Nadal two years ago and will next meet Monfils, who advanced to the quarterfinals of this premier clay court event for the first time in nine visits.
The 14th-seeded Monfils had twice reached the third round at this event, including a loss to Federer at this stage in 2008.
Also Thursday, fourth-seeded Milos Raonic of Canada outlasted Spain's Tommy Robredo, 6-3, 3-6, 6-3 and will next play sixth-seeded Tomas Berdych, a 7-6 (9-7), 6-4 winner over Spain's Roberto Bautista Agut.