Rafael Nadal and Roger Federer made short work of their opening opponents in Indian Wells on Sunday.
Playing in his first match since losing an epic Australian Open final to Novak Djokovic, two-times champion Nadal beat Argentine Leonardo Mayer 6-1 6-3.
Federer breezed into round three with a 6-4 6-1 win over Denis Kudla of the US.
In the women's draw, second seed Petra Kvitova suffered a shock 2-6 6-2 6-3 loss to American Christina McHale, but top seed Victoria Azarenka progressed.
"She started off serving really well," said 19-year-old McHale, the 32nd seed. "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."
Azarenka thrashed 25th seed and former French and US Open champion Svetlana Kuznetsova 6-1 6-2 in exactly an hour, saying: "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."
Fifth seed Agnieszka Radwanska overcame 27th seed Flavia Pennetta 6-4 6-2, but ninth seed Vera Zvonareva withdrew due to a viral illness that has affected both players and fans in Indian Wells.
Federer has been struggling with a flu bug and slight temperature but saw off 19-year-old Ukraine-born American Kudla in just 57 minutes.
"I'm always relieved and happy when I am able to find my way into a tournament," said Federer, who should face a tougher test against Canadian 27th seed Milos Raonic in round three. "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."
Nadal showed no ill effects on his return to competitive action as he dominated Mayer to set up a meeting with fellow Spaniard Marcel Granollers, a 6-3 2-6 6-3 winner over Tommy Haas.
World number two Nadal, who took February off to rest his shoulder, said: "Very happy to be back in competition, that's the first thing. 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."
Former US Open champion and ninth seed Juan Del Potro beat Australian Marinko Matosevic 7-5 6-2, while Fernando Verdasco was too strong for Ryan Sweeting, winning 6-2 6-2.
In the doubles, Andy and Jamie Murray beat fellow Brits Colin Fleming and Ross Hutchins 13-11 in a match tie-break.