Nadal, making his first appearance since losing to world number one Novak Djokovic in an epic Australian Open final in January, showed no signs of rust in winning his second-round clash 6-1 6-3 against Leonardo Mayer in 75 minutes.
The second-seeded Spaniard got off to a strong start and never looked threatened in claiming the opener and, although Argentinian Mayer put up more of a fight in the second set, he lacked the tools to genuinely test the 10-time grand slam champion.
"Very happy to be back in competition, that's the first thing," Nadal said on www.bnpparibasopen.com. "This is a tournament that I love. I really enjoy playing this tournament. Always in my career, I had good success here. I played very good matches.
"It's nice to be back playing at the very good level. 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."
Next up for Nadal will be 26th seed Marcel Granollers, who beat Tommy Haas 6-3 2-6 6-3.
Third seed Federer also breezed into round three, converting five of his six break opportunities to see off the challenge of 19-year-old Ukraine-born American Denis Kudla 6-4 6-1 in 57 minutes.
"I'm always relieved and happy when I am able to find my way into a tournament," Federer said. "So 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."
The Swiss will play Milos Raonic in round three after the 27th seed from Canada toppled Argentina's Carlos Berlocq 6-4 6-2.
Kvitova, meanwhile, looked to be heading for an equally routine victory in her women's third-round match when she won the first set against 19-year-old Christina McHale, but the American 32nd seed battled back to stun the third-seeded Czech 2-6 6-2 6-3.
McHale said: "She started off serving really well. I couldn't get a read on her serve in the first set, and I wasn't moving very well, either.
"And then I just hung in there early in the second, and then she played one service game where she gave me a couple of loose errors, and then I just kept hanging in there. Then I got more comfortable as the match went on."
McHale will face 18th seed Angelique Kerber in the last 16, the German going through after Vania King withdrew with an illness which is reportedly troubling others at the event.
There were no such worries for Victoria Azarenka, the top seed ousting 25th seed Svetlana Kuznetsova 6-1 6-2 in exactly an hour.
The world number one from Belarus said: "I knew she was going to be dangerous.
"She's a grand slam winner. I really had to step it up from my last match, and I'm glad I could perform much better than I did in that first match."
Klara Zakopalova advanced when her opponent, ninth seed Vera Zvonareva, withdrew due to a viral illness, while fifth seed Agnieszka Radwanska overcame 27th seed Flavia Pennetta 6-4 6-2.
Also in the women's event, French Open champion Li Na beat fellow Chinese Zheng Jie 6-1 6-3, big-hitting German Julia Goerges saw off Spaniard Anabel Medina Garrigues 6-3 6-4 and Jamie Hampton battled past Jarmila Gajdosova 6-2 6-7 (1/7) 6-2.
Elsewhere in the men's event, fifth-seeded Spaniard David Ferrer cruised past Bulgaria's Grigor Dimitrov 6-2 6-2 and was joined in round three by sixth seed Jo-Wilfried Tsonga, who led Michael Llodra 4-1 when his fellow Frenchman retired with a knee injury.
Ninth seed Juan Martin Del Potro also eased into round three with a 7-5 6-2 defeat of Australian qualifier Marinko Matosevic, while 10th seed Janko Tipsarevic got past Luxembourg's Gilles Muller 6-4 6-2 and former world number three Nikolay Davydenko accounted for lucky loser Bjorn Phau 7-5 6-2.
Fernando Verdasco, seeded 19th, had few difficulties in brushing aside Ryan Sweeting 6-2 6-2 and 28th seed Radek Stepanek outclassed Xavier Malisse 6-2 6-1, but 21st seed Alexandr Dolgopolov was made to work harder before overcoming Steve Darcis 6-7 (13/15) 6-3 7-5.
Four seeds did go out in the men's draw, however, with Marcos Baghdatis toppling 15th seed Feliciano Lopez 6-3 6-4, David Nalbandian scraping past 24th seed Marin Cilic 7-6 (7/3) 7-6 (7/4), Denis Istomin edging out 31st seed Juan Ignacio Chela 7-6 (7/5) 6-7 (7/9) 7-5 and Thomaz Bellucci seeing off 20th seed Jurgen Melzer 6-3 6-3.
In the men's doubles, Andy and Jamie Murray advanced to the second round after beating Colin Fleming and Ross Hutchins.
The brothers achieved a three-set triumph over Fleming and Hutchins.
The four Britons put on an entertaining display in a closely-contested encounter on Court Seven, the Scottish brothers eventually prevailing 3-6 6-2 13-11 on the match tie-break.
Andy Murray, who suffered a shock exit in the singles second round at the hands of world number 92 Guillermo Garcia-Lopez on Saturday night, sealed victory with a forehand return after Fleming and Hutchins had failed to convert two match points.