The 35-year-old, with eight grand slam titles and a fragile back, is the principal US hope in the men's singles after the shock exit of Andy Roddick and his 7-6, 7-6, 7-6 win was a lesson in how to counter the skewering serve of a 2.08m opponent.

"It was good to close that one out, it was only getting tougher," seventh seed Agassi, who stands 1.80m tall, told an adoring Arthur Ashe Court crowd.

"It's an incredible serve. I'm trying to figure out where it is I would need to have to stand on the court to have the same trajectory. You're sort of diving, but then you can't reach it, even if you dive perfectly and on cue."

If Agassi had to scrap for every point, the same could not be said of the leading women's contenders.

Second seed Lindsay Davenport, third seed Amelie Mauresmo of France and Belgian number seven Justine Henin-Hardenne advanced to the third round with almost embarrassing ease.

Davenport thrashed French qualifier Pauline Parmentier 6-1, 6-1 and Mauresmo hammered Bulgaria's Sesil Karatantcheva 6-0, 6-1.

Henin-Hardenne, the 2003 winner and reigning French Open champion, won 6-3, 6-4 against Spain's Maria Sanchez Lorenzo.

Karlovic caused one of the biggest shocks in tennis history when he knocked then-defending champion Lleyton Hewitt out of Wimbledon in the first round in 2003.

Agassi had never played him before but simply bided his time, waiting for the tiebreaks before raising his game in a style befitting one of the game's all-time greats.

The scoreline in Davenport's match was misleading.

The American got only 49 percent of her first serves in and made 19 unforced errors, only one less than her 253rd-ranked opponent.

Mauresmo's evening session contest was another mismatch, with 16-year-old Karatancheva apparently still feeling the effects of a three-set, first round win.

In round three, Henin-Hardenne plays Cho Yoon-jeong of South Korea, who upset Argentine 27th seed Gisela Dulko 6-4, 6-3.

"I had little ups and downs but a lot of good things," said Henin-Hardenne, who is nursing a sore hamstring.

Sixth seed and last year's runner-up Elena Dementieva of Russia beat Argentina's Mariana Diaz-Oliva 7-5, 6-1, despite serving 11 double-faults.

This year's French Open runner-up Mary Pierce, seeded 12, was a 6-3, 6-2 winner over Slovenia's Katarina Srebotnik.

The first 12 of Thursday's 16 scheduled women's second round matches were decided in straight sets and Davenport blamed the system of having 32 seeds in grand slams, as opposed to 16, for the lack of competitiveness.

In-form American Robby Ginepri exacted revenge for the host nation when he battered Luxembourg's Gilles Muller 6-1, 6-1, 6-4 in the men's second round.