Nadal is chasing a ninth Roland Garros title in 10 years and the Spaniard was in ominous form as he beat Austria's Dominic Thiem with consummate ease in a 6-2 6-2 6-3 win on the famous red clay on Thursday.
Thiem, tipped for a promising future, showed positive signs with 27 winners, but 41 unforced errors meant Nadal - who broke seven times - was a comfortable winner on Court Philippe Chatrier.
The world number one continues his quest for a 14th grand slam title against world number 65 Leonardo Mayer after the Argentinian defeated Teymuraz Gabashvili 6-2 4-6 6-4 6-4.
Fifth seed Ferrer continued his latest attempt to win a first grand slam crown by disposing of Italian Simone Bolelli 6-2 6-3 6-2 in under two hours.
The Spaniard was runner-up to Nadal 12 months ago and could potentially face his compatriot again in the quarter-finals.
However, in round three the 32-year-old faces a tricky task in the form of Andreas Seppi. The 32nd seed was a comfortable 6-2 6-4 6-4 winner against Juan Monaco.
Wimbledon champion Murray set up a third-round tie with Philipp Kohlschreiber as he breezed past Australian Marinko Matosevic 6-3 6-1 6-3.
Matosevic - who won his maiden first-round match at a grand slam at the 13th attempt against Dustin Brown on Tuesday - had no answer the Scot's superiority.
The seventh seed was particularly impressive on Matosevic's serve, earning 19 break points and converting six to confirm his progression.
Murray should face a sterner challenge against 28th seed Kohlschreiber. The German - who won his first title of the year in Dusseldorf last week - ousted Denis Istomin.
The partisan home crowd were also treated to a double success as Richard Gasquet and Gael Monfils, seeded 12th and 23rd respectively, emerged from their matches unscathed.
Gasquet - who has never gone beyond round four in Paris - saw off Argentinian Carlos Berlocq 7-6 (7-5) 6-4 6-4, while Monfils defeated Jan-Lennard Struff 7-6 (7-4) 6-4 6-1.
Fernando Verdasco plays Gasquet next, the 24th seed winning a five-set epic against Pablo Cuevas 4-6 6-7 (6-8) 7-5 6-4 6-3, while Monfils faces a tricky test against 14th seed Fabio Fognini, the Italian safely beating Thomaz Bellucci 6-3 6-4 7-6 (7-2).
South Africa's Kevin Anderson, seeded 19th, will face Ivo Karlovic in round three, the former having overcome Axel Michon, while the latter saw off the challenge of Andreas Haider-Maurer.
Feliciano Lopez was a surprise casualty, however, the 26th seed falling to a 6-3 7-6 (7-1) 6-3 defeat to Donald Young, the American rewarded with a third-round contest against another Spaniard in the form of Guillermo Garcia-Lopez, who defeated home favourite Adrian Mannarino in four sets.
Other second-round winners included Dusan Lajovic and Jack Sock.