The world's No. 1 player needed just 52 minutes to reach the third round of the $1.2 million tournament, where Venus Williams and Jennifer Capriati are entered.

Williams is No. 2 and closing in on the Swiss star's top ranking. Capriati is No. 4 and rising quickly after winning the Australian Open.

``I want to stay up where I am and I'm not giving that up for anybody,'' said Hingis, who could be passed by Williams at the French Open, which begins May 28.

Williams and Capriati, on the same side of the draw, begin play Wednesday. Hingis' path to the final got easier when 10th-seeded Kim Clijsters was ousted 6-2, 6-1 by Luxembourg's Anne Kremer.

The Belgium teen-ager, also climbing the rankings, beat Hingis last month in the Indian Wells semifinals.

In other matches, eighth-seed Arantxa Sanchez-Vicario of Spain advanced with a 6-3, 6-3 win against Ai Sugiyama of Japan, and 14th-seeded Sandrine Testud of France ousted Marlene Weingartner of Germany 7-6 (4), 6-2.

Meghann Shaugnessy, a finalist at Hamburg last week, knocked out Elena Likhovtseva of Russia 6-1, 6-4, and Denisa Chladkova of Czech Republic beat 12th-seeded Chanda Rubin.

Hingis had given up only two games in two previous matches against Garbin, ranked No. 56. But she struggled occasionally in her first match this season on European clay.

She started the second set by losing the opening game with a double fault and a missed forehand. However, she proved too steady for Garbin.

Hingis said she felt comfortable in her first match since Capriati edged her in three sets in the Charleston, S.C., final two weeks ago.

``I've been working very hard the past two weeks ago,'' Hingis said. ``I've been practicing more and I'm willing to spend more time out there.''

Hingis raced to three titles in her first five events in 2001. But she hasn't captured any of her last four, losing to Williams and Capriati.

This is her third tournament without a coach and without her mother sitting courtside. She is accompanied by Australian David Taylor, her hitting partner.

The last time Hingis played without her mother at a Grand Slam event was Wimbledon in 1999, when she lost in the first round.

``I feel this is a little different than Wimbledon,'' she said. ``This time I gave myself a little time to adjust,'' said Hingis.

Yugoslav teen-ager Jelena Dokic, who stunned Hingis with the Wimbledon first-round exit, won 6-2, 3-6, 6-4 victory against Zimbabwe's Cara Black. Also, Austria's Barbara Schett slipped past Sweden's Asa Carlsson in three sets.