Six-times champion Andre Agassi began his 19th Nasdaq-100 Open campaign with a 7-5 6-4 second-round win over Paul-Henri Mathieu of France on Sunday.
World number one Roger Federer also came through sweltering conditions to beat Belgian Olivier Rochus 6-3 6-1. Amelie Mauresmo, the top seed in the women's event, had a fright before putting out Russian Maria Kirilenko 4-6 6-4 6-1.
Ninth seed Agassi had to wait until the end of the first set to break Mathieu's resistance but once he had taken the lead he showed little sign of surrendering it.
The 34-year-old American, who was watched by his wife Steffi Graf, shrugged off pre-tournament worries about his injured toe.
"I felt it a little bit but when I pushed through it never got worse, so that was reassuring," Agassi told reporters.
"It was a tough match. There's nothing I take for granted out there, especially not these days, and it was a good one to get through."
Federer needed only 71 minutes against Rochus to extend his winning streak to 17 matches.
The Swiss has now won 43 of his last 44 contests, stretching back to last August's U.S. Open. His one defeat this season was at the hands of Russian Marat Safin in the semi-finals of the Australian Open in January.
Since then Federer has won consecutive titles in Rotterdam, Dubai and, last week, at Indian Wells.
Unseeded Kim Clijsters also kept up her hot streak by overcoming American Amy Frazier 6-2 6-3.
The former world number one from Belgium, playing her third event since missing most of 2004 with a wrist injury, has lost only one of her 12 matches since launching her comeback last month.
Last week Clijsters won the Pacific Life Open title at Indian Wells. Her victory over Frazier was her ninth in a row and set up a third-round clash with Frenchwoman Nathalie Dechy.
"I'm working hard and I'm feeling very fit out there," said Clijsters.
Britain's Tim Henman also progressed with an efficient 6-3 7-5 triumph over Czech Ivo Minar.
"It's really hot out there. Those are conditions where you don't want to be out there any longer than necessary," said sixth seed Henman.
Last year's runner-up, fourth seed Guillermo Coria, safely negotiated his match with Davide Sanguinetti, beating the Italian 6-1 6-4.
Argentina's Coria had to retire from last year's final against Andy Roddick with back pain.
Defending champion Roddick had to pull out of the tournament on Friday with a wrist injury.
Australian Mark Philippoussis withdrew on Saturday after sustaining a sprained left ankle in his first-round win over Rochus's brother Christophe earlier this week.
Mauresmo said she might have benefited in her match with Kirilenko from the 10-minute break players are given before the third set under the WTA Tour's extreme heat rule.
"I was capable of coming back on court after the break and really being able to give 100 percent. Maybe it wasn't really the case for her," said Mauresmo.
"She played really well in that first set especially. It took me a little time today and I finally got my game together."