The Associated Press

NEW YORK - Jennifer Capriati and Mary Pierce know all about the highs and lows of pro tennis.

Both have been Grand Slam tournament champions - more than once. Both have gone significant stretches without winning any sort of title: Capriati recently ended her 1 1/2-year drought, while Pierce's dates to 2000. Both have been ranked highly and have slipped out of the top 100.

Through it all, each kept her head up and slugged the ball.

Faced with a 5-1 third-set disadvantage Thursday at the U.S. Open against No. 22-seeded Jelena Dokic, Pierce mustered just enough power and gumption to pull out a 6-2, 6-7 (5), 7-6 (5) victory and reach the third round.

"I'm still not back to the level where I want to be," Pierce said. "... The fitness and my physical level are getting better, but it's not there yet."

Andre Agassi, at 33, had no trouble keeping up despite being the oldest No. 1-ranked player in ATP Tour history. He was challenged early by Andreas Vinciguerra but put together a tidy 7-6 (1), 6-1, 6-4 victory.

Agassi next faces two-time major champion Yevgeny Kafelnikov.

Capriati easily defeated Martina Sucha 6-1, 6-1. The only games Capriati lost were on her own serve, and she double-faulted five times.

"I miss being at the top and playing good tennis," said Capriati, who won a tuneup event last week, her first title since the 2002 Australian Open.

She was in control throughout Thursday, whipping deep strokes to compile a 28-4 edge in winners.

According to Dokic, no one hits the ball harder than Pierce.

"Some of the shots she hit," Dokic said, "I didn't see."

That might have been how Todd Martin felt as he tried to deal with French Open runner-up Martin Verkerk's serves, which consistently topped 130 mph.

But Martin, the 1999 U.S. Open runner-up, withstood the Dutchman's 26 aces - which were counterbalanced by 12 double-faults - and eliminated the 16th-seeded Verkerk 6-3, 6-4, 6-7 (5), 7-6 (9).

Dokic and Verkerk were among a sizable group of lower-seeded players exiting in second-round action Thursday - including No. 24 Mardy Fish, knocked off by Karol Kucera 6-4, 7-6 (7), 6-4. Kucera won despite getting treated for back pain in the third set.

No. 23 Wayne Ferreira was sent packing by American Robby Ginepri, who lost to Andy Roddick in the 2000 junior Open final. Ginepri advanced to the third round of a major for the first time by beating Ferreira 6-2, 6-4, 6-7 (0), 6-2.

Seeded players advancing included major title owners Justine Henin-Hardenne, Lleyton Hewitt and Juan Carlos Ferrero.

Pierce made her Grand Slam breakthrough at the 1995 Australian Open, and she added a second major title at the 2000 French Open. But back, shoulder, abdominal, ankle and groin ailments forced her off the tour for 10 months the past two seasons.

With her final-set deficit against Dokic, Pierce let instinct take over. Pierce, who later said she wasn't quite sure of the score, reeled off five straight games to lead 6-5 in the last set. Dokic tied it with two second-serve aces.

Then, at 5-5 in the tiebreaker, Pierce smacked a cross-court backhand winner at a tough angle to get to match point. She raised both hands, threw her head back, and closed her eyes. Pierce lifted her index fingers to the sky and said, "One more!"

She got one more point when Dokic floated a forehand wide.

"I just tried to stay calm and just told my myself to fight. Just kept repeating that one word to myself," Pierce said.

Yesterday's rising star can turn into today's has-been, and Dokic could be treading that ground. She was a Wimbledon quarterfinalist at 16 and a semifinalist at 17. Now 20, she entered the Open with a sub-.500 record this year.

"Sometimes," Dokic said, "you need to really go down to come back up even stronger."