Novak Djokovic survived a few sticky moments on his way to an opening win over Victor Hanescu at the BNP Paribas Open but Tomas Berdych and Juan Martin del Potro bowed out.
Rafael Nadal and Andy Murray both lost the first sets of their opening matches at Indian Wells in California, USA, and Djokovic had to save two set points before pulling away to win 7-6 (7/1) 6-2.
The second seed, who next meets Alejandro Gonzalez, said: "It's one of those days where you get to serve well and everything else is just trying to find the way to play the right shots at the right time.
"I didn't make any returns in the first set. Second set I also struggled with the return, which is one of my better shots in the game.
"It's the first match and it takes a little bit of time to get used to the centre court."
Fourth seed Berdych became the highest-ranked casualty on the men's side so far as he crashed out 4-6 6-2 6-4 to Spain's Roberto Bautista Agut.
Bautista Agut also upset Del Potro at the Australian Open in January, but Berdych felt most of the blame lay with him.
He said: "Anything I touched today was basically bad and was wrong. It was definitely my worst match that I had this year."
Del Potro did not even take to the court for his scheduled match against Feliciano Lopez.
The sixth seed, who reached the final last year, has been struggling with a left wrist problem and felt it was not worth risking further damage.
Twelfth seed John Isner ensured one American man reached the third round from 14 who started the tournament with a 7-6 (7/5) 6-3 victory over Nikolay Davydenko.
Jo-Wilfried Tsonga's struggles continued as he fell 6-4 6-4 to French compatriot Julien Benneteau in the night session.
In the women's tournament, second seed Agnieszka Radwanska was ruthless in dispatching talented young German Annika Beck 6-0 6-0.
Radwanska was not entirely convincing in beating Heather Watson in round two but was totally in control on Sunday to set up a fourth-round meeting with Alize Cornet.
The Frenchwoman was involved in a marathon on Stadium 4, taking almost three and a half hours in beating Carla Suarez Navarro 6-7 (4/7) 7-5 6-3.
Eugenie Bouchard continued her rise by easing to a 6-3 6-3 win over ninth seed Sara Errani to reach the fourth round.
The Romanian sixth seed has had a remarkable last 10 months but had to battle her way to 6-2 4-6 6-4 win over Czech Lucie Safarova.
Tenth seed Caroline Wozniacki was also taken the distance by Yaroslava Shvedova but pulled away in the decider to win 7-6 (9/7) 3-6 6-1.
American 20-year-old Lauren Davis followed up her upset of Victoria Azarenka by defeating countrywoman Varvara Lepchenko while Roberta Vinci's tally of singles victories this year stayed at one as she lost to Australian Casey Dellacqua.