JOIN USWorld number one Nadal, losing finalist to Novak Djokovic at Indian Wells, California, defeated compatriot Feliciano Lopez for the seventh time in nine matches, 6-3, 6-3. Federer, seeded third, played a tight first set but broke it open in the second to defeat clay-courter Juan Monaco 7-6 (7-4), 6-4.
The Federer used his all-court game to expose the limitations of the Argentine, whom he last played four years ago.
"You're trying to mix up the game to see how he reacts to shorter rallies, to shots hit shorter and longer, instead of always going laterally. I was able to do that," Federer said.
"He struggled a bit with that, because he's a very good rhythm player. I kept the points short, because I thought he doesn't quite like that - that's how I like to play."
Nadal, twice a losing finalist, has reached the quarter-finals or better in five of seven attempts at Miami.
Seventh-seeded Wimbledon finalist Tomas Berdych defeated Carlos Berlocq 7-6 (10-8), 7-5.
German players split in Miami, with Florian Mayer putting out 11th seed Nicolas Almagro 6-1, 3-6, 6-1, while Serb Janko Tipsarevic stopped Philipp Petzschner 6-3, 6-3.
In the women's draw, Germany's Andrea Petkovic sent top seed Caroline Wozniacki out 7-5, 3-6, 6-3.
Petkovic became the first German woman to defeat a number one in a completed WTA match since Steffi Graf beat Martina Hingis in the 1999 French Open final.
"It was not like I played unbelievable," said the winner. "It was more that I was able to stick to my game plan, and I was playing clever. That was the key to the match."
Russian third seed Vera Zvonareva turned around a losing cause to defeat French 15th seed Marion Bartoli 2-6, 6-3, 6-2.
Number six Jelena Jankovic was untroubled by Spain's Anabel Medina Garrigues 6-1, 6-3. Russian 16th seed Maria Sharapova staged an upset of her own with a defeat of Australian fourth seed Samantha Stosur 6-4, 6-1.
The 23rd-ranked Petkovic, who lost an Australian Open quarter-final to eventual finalist Li Na, needed an hour to lift the opening set as she fired an ace to clinch the early lead.
Wozniacki, who had been bidding for the US spring double after winning Indian Wells a week ago, claimed the second, but her German opponent hung tough in the third.
Petkovic sent up a break for 4-2 as the top seed from Denmark netted a backhand. The challenger stayed the course and served out the victory three games later with her third ace, after saving a dozen of 17 break points she faced on the afternoon.
The seed finished with a massive 52 unforced errors.
"Nothing was going on with my forehand, nothing was going on with my backhand," said Wozniacki.
"I lost the match. She played a good match. I've been playing a lot of matches, but I've been doing so well. Today I just took some wrong decisions."