MELBOURNE, Australia -- Once again, Serena Williams had a slow start but a strong finish, moving within three victories of capturing the Australian Open championship and a "Serena Slam.''

Williams, who already holds the most recent titles from the French Open, Wimbledon and U.S. Open, beat Eleni Daniilidou 6-4, 6-1 Monday.

Her quarterfinal opponent will be fellow American Meghann Shaughnessy, who saved five break points in the final game to beat Elena Bovina 5-7, 6-2, 6-4.

"That's a great win for her,'' Williams said of Shaughnessy. "OK, that's two Americans in the quarterfinals, so one of us is guaranteed to get to the semis.''

Also in the quarterfinals is Williams' sister Venus, who lost to Serena in the final three Grand Slam events last year.

Williams played the last match on center court before organizers suspended play on the outside courts, citing temperatures of 95 degrees and high humidity. They had the option of closing the roof over center court.

"It's hard to breathe,'' said Williams, who sat gulping air during the changeovers. "But it's OK, I like the heat.''

Williams, who missed the Australian Open with an injury last year before winning three straight majors, has struggled at the beginning of three of her four matches here so far. In Monday's first set, she gestured in exasperation over some of her misses.

Her serve was broken twice in the set, but she broke three times. The 20-year-old Daniilidou, who's from Greece and was seeded 18th, helped by double-faulting eight times.

Williams then settled down, reducing her errors from 21 in the first set to six in the second.

"I always say, `OK, keep trying,' Williams said. "I got out to a slow start, which is something I don't want to happen'' as the matches get tougher.

Shaughnessy, a 23-year-old American who's seeded 25th, reached the quarterfinals of a Grand Slam event for the first time by winning her 11th straight match to start the year. Before the Australian, she won a warmup tournament in Canberra.

Serving for the match against Bovina, a U.S. Open quarterfinalist last year, Shaughnessy saved break points with an error by the 19-year-old Russian, a service winner, an overhead smash, an inside-out forehand and an ace.

After another service winner, she finished the 2-hour, 19-minute match when the 20th-seeded Bovina netted a backhand serve return.

Shaughnessy's previous best showing in a major came at the 2001 French Open and Wimbledon, where she reached the fourth round.

''To beat Serena, you've got to attack her,'' Shaughnessy said. ''She's such a great player it's going to take someone really going after the match.''

Shaughnessy was leading 5-4 against Serena in a warmup tournament last year when Serena twisted her ankle chasing a drop shot and pulled out of the Australian Open.

In other matchs Monday, Fourth seed Kim Clijsters was a model of efficiency as she crushed South African Amanda Coetzer 6-3, 6-1. In the quarterfinals, Clijsters will play No. 8 seed, Anastasia Myskina, who posted a 4-6, 6-4, 6-1 victory over 10th-seeded Chanda Rubin.