Top seed Nadal, champion at eight of the last nine editions, spent 72 minutes in smothering any hopes of an upset by Russian Teimuraz Gabashvili, who got off to a shock 3-1 lead before Spain's king of clay reeled him in for a 6-4, 6-1 success.
Federer, seeded fourth at the Masters 1000 event that he has never won, delivered a 6-1, 6-2 thrashing to fellow veteran Radek Stepanek.
Federer's rout in 52 minutes was seven minutes longer than another easy victory by holder Novak Djokovic a day earlier.
"I was able to get a lot of returns back into play," said Federer. "On clay, when you have the upper hand from the baseline, it's kind of hard to get out of it. It was clearly a good match to start my claycourt campaign."
The Swiss will next face off for a quarter-final spot on Thursday when he takes on Lukas Rosol.
The Czech booked his spot over Frenchman Michael Llodra 6-4, 6-4.
Federer improved to 14-2 over Stepanek, 35, whose last victory in the series came in Rome six years ago.
The winner was aided by five Stepanek double-faults, with Federer breaking four times.
Meanwhile, Nadal steadied after going down early against Gabashvili, with the Spaniard improving to 49-2 at the event.
The top seed will now line up against Andreas Seppi after the Italian defeated Pablo Andujar 7-6 (7/5), 5-7, 6-4.
Federer’s Swiss compatriot Stanislas Wawrinka also registered a comfortable 6-0, 6-2 victory over Marin Cilic and advanced to the next round.
In other matches, Canadian eighth seed Milos Raonic duplicated his best showing in the principality with a 6-7 (4/7), 6-2, 6-1 defeat of Taiwan's Yen Lu-Hsun while Italian 10th seed Fabio Fognini beat Roberto Bautista Agut of Spain 7-6 (8/6), 6-4.
Aisam-Bopanna advance to quarters
Pakistan’s Aisamul Haq Qureshi secured a quarter-finals berth along with doubles partner Rohan Bopanna as the duo posted a comfortable 6-3, 6-0 win over Lukasz Kubot and Robert Lindstedt in the second round.
While seventh seeds Kubot and Linstedt had received a bye in the first round, Aisam and Bopanna had beaten Julian Knowle and Vasek Pospisil 7-6 (7/2), 6-4 in their campaign opener.
The Indo-Pak Express will next meet Jeremy Chardy and Gilles Simon in their last-eight encounter, who defeated Ivan Dodig and Marcelo Melo to reach the quarter-finals.
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