Williams, who will regain the No. 1 ranking if she reached the semifinals, showed no signs of the back or ankle injuries that troubled her at the Australian Open during her 6-2, 6-1 win over Russian qualifier Daria Gavrilova.
“I have it heavily taped. As long as the tape doesn’t get loose, it feels really good,” the 15-time Grand Slam winner said. “Physically feeling better is so good, and hopefully I can stay on that level.”
The third-ranked Sharapova, who won the tournament in her two previous appearances, downed French qualifier Caroline Garcia 6-3, 6-2.
American Sloane Stephens, who defeated Williams at the quarterfinals of the Australian Open, beat Anna Tatishvili 6-2, 6-2. Stephens pulled out of Fed Cup against Italy last week after aggravating an abdominal muscle injury and suffering from a stomach virus.
“I hadn’t really been serving since my ab was a little sore,” Stephens said. I didn’t serve that great today. “Actually last weekend I got like, I don’t know, like a stomach virus or something. ... I’m just happy that I can play now.”
Williams broke Gavrilova to go up 4-2 in the first set and took a 5-0 lead in the second. Williams then saved five break points before serving out the match when the 160th-ranked Gavrilova hit a forehand long.
Williams acknowledged she has to do better on her first serve, which is considered among the best in the women’s game. She hit the mark just over half the time.
“I wasn’t making my first serve today,” she said. “It’s always something I can work on and try to do better in my next round.”
Sharapova broke the 172nd-ranked Garcia twice go up 3-0 in the first set. Garcia won the next two games but Sharapova broke for a third time. The second set went with serve through the first five games until Sharapova broke to go up 4-2, and she clinched the win when the Frenchwoman hit a forehand long.
“I was quite happy with the way I played, because my opponent has already played a few matches here so she’s been able to get in that match atmosphere,” Sharapova said. “So I wanted to start really strong. I had a tough match against her in my previous encounter where I played three sets. I really wanted to start better this time as opposed to last time.”
Sharapova was joined in the third round by 11th-ranked Marion Bartoli, who downed former French Open champion Francesca Schiavone 7-6 (5), 6-3. The loss leaves Schiavone, who has fallen to 54th in the rankings, winless in four matches this year.
Sixth-ranked Angelique Kerber became the first top player to be eliminated from the tournament, routed by fellow German Mona Barthel 6-1, 6-2 in just more than an hour.
Schiavone had the upper hand early, taking a 4-1 lead. But Bartoli turned things around, saving five break points to make it 4-2 breaking back in the next game when Schiavone doubled faulted. She won the tiebreaker with a return winner.
After trading breaks early in the second set, Bartoli took advantage of Schiavone’s errors to go up 4-2. She closed out the match when she chased down a volley and fired a backhand winner down the line.
“The first set was extremely tough,” Bartoli said. “It was a hard battle. I knew from coming from indoor clay court I wouldn’t play my best tennis for the first 30 minutes. ... But I felt I really fought really hard on the court. I didn’t show any frustration.”
The only other seeded player to lose Tuesday was No. 12 Maria Kirilenko of Russia, who retired with a right shoulder injury against fellow Russian Ekaterina Bychkova after trailing 3-0.
Yanina Wickmayer of Belgium also withdrew from the tournament with a lower back injury, as did Varvara Lepchenko of the United States with an upper respiratory illness.
Lepchenko won two matches for the U.S. team in its 3-2 loss to Italy in the Fed Cup on Sunday.