Spaniard Nadal ruthlessly dealt with Argentine Leonardo Mayer 6-1, 6-3 before Swiss maestro Federer eased past American wild card Denis Kudla 6-4, 6-1 in the evening session at the Indian Wells Tennis Garden.
Left-hander Nadal, who has reached the semifinals at Indian Wells in his last six appearances, broke Mayer twice in each set to wrap up a commanding win in one hour, 15 minutes.
In dazzling afternoon sunshine, the match ended when a Mayer forehand sailed wide and Nadal removed his green headband in triumph as the near-capacity crowd erupted in applause.
"It's nice to be back playing at the very good level," the Spaniard, who will next face compatriot Marcel Granollers, told reporters. "Winning is the most important thing.
"It's not easy to be back after a while without competition, but I did really well. I started the match very focused, very aggressive. I'm very happy about almost everything." Nadal, who dominated Mayer with his crunching ground strokes from behind the baseline, had not competed since he lost an epic Australian Open final to Novak Djokovic in January.
The world number two enjoys a superb record at Indian Wells where he won the title in 2007 and 2009 and was beaten in last year's final by Serb Djokovic.
"This is a tournament that I love," said the 25-year-old from Mallorca. "I enjoy a lot playing this tournament. Always in my career I've had good success here. I have played very good matches." Granollers had earlier booked his place in the third round with a 6-3, 2-6, 6-3 win against Germany's Tommy Haas.
World number three Federer, who is shaking off a flu bug and slight temperature, broke Kudla twice in the opening set and three times in the second to wrap up a one-sided victory in under an hour.
"I'm always relieved and happy when I am able to find my way into a tournament, see where you're at," said the 16-times grand slam champion, whose entire family has been sick.
"It's a good start for me. I didn't know Kudla very much, or at all really, so it was a good win for me. I'm looking forward to what's next." Federer, who won three consecutive titles at Indian Wells from 2004, next faces towering Canadian Milos Raonic, a 6-4, 6-2 winner against Argentina's Carlos Berlocq.
Asked how he felt health-wise, Federer replied: "I have a bit of a combination (of flu and a cold). Not a terrible temperature, but I have some things going on. But I'm the best off in my family... the rest of them are struggling much more." In other matches, fifth-seeded Spaniard David Ferrer crushed Bulgarian Grigor Dimitrov 6-2, 6-2, David Nalbandian of Argentina battled past Croat Marin Cilic 7-6, 7-6 and Serb Janko Tipsarevic beat Gilles Muller of Luxembourg 6-4, 6-2.
Sixth seed Jo-Wilfried Tsonga advanced when fellow Frenchman Michael Llodra retired hurt because of a knee injury when trailing 4-1.
The big-serving Tsonga will next face Czech Radek Stepanek, who crushed Belgium's Xavier Malisse 6-2, 6-1.
