Sharapova, playing her first match since Wimbledon, defeated fellow Russian Vasilisa Bardina 6-4, 6-1 while Hingis beat Meilen Tu 6-2, 6-3 in her first Southern California match since 2001.
I'm excited going into a tournament feeling healthy and playing pretty well," Sharapova said. "It's a matter of getting into the matches again. I'm happy to win the first round, but there's a long way to go."
Beating Bardina was just the first step Sharapova expected.
"I felt good. We had some long rallies at the start," she said. "But after she broke me in the first set, I made her play a bit and put pressure on her. I felt really good out there."
Five-time Grand Slam winner Hingis, who came back to the sport after a three-year absence, advanced after a first-round bye in 66 minutes over the 91st-ranked American.
Hingis turned back the clock and improved to 15-3 at the tournament. She staved off six break points while breaking three times in the comfortable victory.
In their junior days, Tu beat Hingis in the final of the 2004 US Open juniors, a match which Hingis certainly recalls. But her game has moved on in the past dozen years.
"When they were reading my accomplishments in the (pre-match) warm up, it sounded like a fairytale," said 13th-ranked Hingis. "That was a part of my life.
"When I left tennis and did something else, that was another part, But now, I feel more like a rookie again rather than a comeback."
Hingis next plays either Italy's Flavia Pennetta or American Jamea Jackson.
The eighth-seeded Swiss won the tournament on her debut as a teenager during the magical 1997 season in which she lifted three of the four majors.
Her last appearance was a semi-final run five years ago against Monica Seles.
