Hingis, the top seed, continued to march toward her first title at Roland Garros by disposing of Italy's Tathiana Garbin, 6-1, 6-0, in 54 minutes.
The player Hingis was named after, Martina Navratilova, was victorious in her first French Open appearance since 1994.
Competing in her second tournament since coming out of retirement last week, the 43-year-old Navratilova teamed with South Africa's Mariaan de Swardt to defeat Sabine Appelmans of Belgium and Rita Grande of Italy, 5-7, 6-1, 6-3, in a first-round doubles match.
A two-time singles champion and seven-time doubles winner at the French Open, Navratilova is playing doubles in four tournaments as part of her comeback, although she has stated that she is playing for fun rather than winning titles.
After playing in Paris, Navratilova will compete at a grasscourt event in Eastbourne, England before attempting to tie Billie Jean King for the most overall Wimbledon titles with 20 later this month.
One day after the elimination of men's defending champion Andre Agassi, 1996 winner Yevgeny Kafelnikov of Russia received a scare before winning his third straight match.
After struggling through five-set matches in the first two rounds, Kafelnikov fought off Frenchman Sebastien Grosjean, 6-3, 6-1, 5-7, 6-4, to advance to the round of 16.
Fifth seed Gustavo Kuerten of Brazil had a surprisingly tough time with Michael Chang before overcoming the American, 6-3, 6-7 (9-11), 6-1, 6-4, in the battle of former French Open champions.
Chang, whose only Grand Slam title came on the red clay in 1989, has not won a tournament in over two years. But he gave Kuerten all he could handle in one of the better matches he has played in quite some time by approaching the net and attacking Kuerten's second serve early on.
Chang saved two set points in the thrilling second-set tiebreaker and leveled the match. Unfortunately, the 28-year-old Chang ran out of gas in the final two sets as Kuerten, the 1997 champion, prevailed in just under three hours.
"I still love going out there and working hard," Chang said. "I believe honestly, in my heart, that better things are to come. Even though I lost today's match, I feel like I lost it in a way that makes me feel good inside. To be able to walk off the court knowing that I had a great chance to win, feels good. It's a great confidence-booster."
In other third-round action, 10th seed and
1998 runner-up Alex Corretja of Spain recorded a 4-6, 6-2, 6-3, 6-2 victory over former Wimbledon champion Richard Krajicek of the Netherlands.
Also, No. 11 Nicolas Lapentti of Ecuador got past Wayne Ferreira of South Africa, 5-7, 6-3, 7-5, 6-3, and No. 16 Juan Carlos Ferrero of Spain advanced when Mariano Puerta of Argentina retired in the second set with a pulled hamstring. Ferrero was leading, 6-2, 3-2.
Fernando Vicente of Spain posted the lone upset on the men's side as he outdueled No. 13 Tim Henman of Britain, 7-5, 4-6, 6-4, 4-6, 6-3.
Unseeded Mark Philippoussis of Australia, who knocked off second seed Pete Sampras in the first round, advanced to the round of 16 at Roland Garros for only the second time by defeating Hicham Arazi of Morocco, 6-2, 6-1, 3-6, 6-3. Philippoussis will battle Ferrero for a berth in the quarterfinals.
On the women's side, third seed Monica Seles of the United States continued to look impressive as she vies for her fourth French Open title. She needed only 49 minutes to eliminate Rita Kuti Kis of Hungary, 6-1, 6-2, and has lost only eight games in her first three matches.
"I've been moving really well," said Seles, who improved to 49-5 lifetime at the French Open. "I've been a lot better getting to balls and in a better position to hit them."
It was a mixed day for seeded Frenchwomen as two advanced and two were knocked out.
Sixth seed Mary Pierce has been dominant in her first three matches. Today the 1994 finalist stormed past countrywoman Virginie Razzano, 6-4, 6-0, and has lost a total of 10 games in the tournament.
No. 13 Amelie Mauresmo of France set up a fourth-round clash with Seles by crushing Kveta Hrdlickova of the Czech Republic, 6-1, 6-0, in 39 minutes. Mauresmo lost to Seles in the final at Rome two weeks ago in a French Open tuneup event.
However, Chanda Rubin of the United States upended seventh seed Nathalie Tauziat, 6-4, 7-6 (7-3) and Asa Carlsson of Sweden outdueled 10th seed Sandrine Testud, 4-6, 6-3, 7-5.