French Open champ Nadal needed just 59 minutes to rout Denis Istomin of Uzbekistan, 6-1, 6-0 while Wawrinka cruised into the fourth round with a 7-5, 6-4 dismantling of Edouard Roger-Vasselin of France at Crandon Park.
"I'm happy with the way I was fighting, the way I stayed positive in the game," said the 28-year-old Wawrinka. "Even if I was wasn't moving or playing so as well at the beginning, I stayed with him.
"I was fighting with myself to get control of the point."
Nadal, who finished runner-up in this event three times, will next face 14th-seeded Fabio Fognini, who battled back to beat Spaniard Roberto Bautista Agut 4-6, 6-3, 6-3.
Swiss Wawrinka will square off against Alexandr Dolgopolov after the 22nd-seeded Ukrainian rallied for a 3-6, 6-0, 7-6 (7/5) win over Dusan Lajovic.
Wawrinka already owns two titles this year. He claimed his first grand slam win in Melbourne in January. His best previous finish in Miami was a straight set loss to Nadal in the round of 16 in 2009.
Like Nadal, Canada's Milos Raonic barely broke a sweat on Monday. Raonic, who dropped only five points on his serve in the match, reached the last 16 for the first time after being forced to withdraw from third-round matches with injuries the past two years.
"I just generally improved, especially on second serve returns (and) taking advantage more of those opportunities," Raonic said.
He next faces German Benjamin Becker, who beat Slovenia's Aljaz Bedene 6-3, 7-5.
"It's going to be a tough match but it's up to me," Raonic said. "I've got to play well. If I do, I can always give myself an opportunity to do well."
Seventh-seeded Tomas Berdych downed Portugal's Joao Sousa 6-2, 6-4, while 10th-seeded John Isner posted a 7-5, 6-3 victory over 18th-seeded Nicolas Almagro of Spain.
The American Isner will face Berdych in the next round.
On the women's side of the draw, world number one Serena Williams breezed into the quarter-finals while Russian fourth seed Maria Sharapova battled through three sets to advance.
Top-seeded defending champion Williams routed US qualifier Coco Vandeweghe 6-3, 6-1 in 78 minutes to book a last-eight matchup with German fifth seed Angelique Kerber.
Sharapova rallied to defeat Belgium's Kirsten Flipkens 3-6, 6-4, 6-1 after two hours and four minutes while Kerber took six minutes longer to eliminate Russia's Ekaterina Makarova 6-4, 1-6, 6-3.
Williams smashed 17 winners to only 11 unforced errors and denied her compatriot on all six of her break-point chances to book her 13th quarter-final in 14 Miami appearances.
"It was a much tougher match than the scoreline showed," Williams said.
Williams owns a 3-1 career edge over Kerber, whose lone win came two years ago on the Cincinnati hardcourts.
"I feel better than I did in my first few matches, though, so I hope I can keep going forward," Williams said.
Four-time grand slam champion Sharapova, a five-time Miami runner-up, is still seeking her first title at the hardcourt event.
"It's not like I didn't have my opportunities in those finals. I just didn't take them. That's why you come back and hope for another chance," Sharapova said.
Sharapova made 10 double faults, half of them in the first set, and served no aces but improved as the match progressed and in the final set won five of 12 points off the Belgian's first serve and seven of nine off her second serves.
Next up for Sharapova will be Czech eighth seed Petra Kvitova who beat Serbian 12th seed Ana Ivanovic 3-6, 6-0, 6-0.
Dominika Cibulkova of Slovakia also advance by beating Venus Williams 6-1, 5-7, 6-3.