Federer fired eight aces against Argentine Diego Schwartzman and didn't face a break point in the 63-minute match, winning by a 6-4, 6-2 final. The second- seeded Swiss star lost to Novak Djokovic in last year's final at Indian Wells.
Nadal, who has won this event three times, cruised past Igor Sijsling, 6-4, 6-2 on the hardcourts at the Indian Wells Tennis Garden.
Sixth-seeded Canadian Milos Raonic defeated Italian Simone Bolelli 6-3, 6-4 to reach the third round, while Robin Haase of the Netherlands stunned seventh- seeded Swiss Stan Wawrinka 6-3, 3-6, 6-3.
Ukrainian Alexandr Dolgopolov, who reached the semifinals last year, topped 29th-seeded Colombian Santiago Giraldo 6-1, 7-6 (7-4).
Americans Steve Johnson, Donald Young and Jack Sock were also among the winners. Johnson upended 21st-seeded Ivo Karlovic (21), 6-3, 7-6 (7-5), Young beat 31st-seeded Frenchman Jeremy Chardy 6-4, 6-2, and Sock rallied for a 3-6, 6-3, 7-6 (9-7) win over Luxembourg's Gilles Muller.