MELBOURNE, Australia — For two sets it looked as if Roger Federer's run at a record 14th Grand Slam title was going to be derailed by Tomas Berdych at the Australian Open.

Then the 6-foot-5 Czech had a meltdown, and Federer swooped, recovering for a 4-6, 6-7 (4), 6-4, 6-4, 6-2 victory Sunday — only his fourth career comeback from two sets down — to reach the quarterfinals.

"You've got to hang in there, there's no other solution," Federer said. "... Tried to weather the storm. He was hitting the ball so heavy and so hard. He pushed me to the limit."

Women's No. 1 Jelena Jankovic had already gone down in straight sets to 2007 Wimbledon finalist Marion Bartoli in the day's first match on Rod Laver Arena. No. 3 Dinara Safina had a narrow escape in the subsequent match, saving match points before fending off another French woman, Alize Cornet, in three.

A massive upset result loomed in the late afternoon when 20th-seeded Berdych was on top for the first two sets, working Federer around with powerful forehands to keep the Swiss star on the defensive. He consistently targeted Federer's backhand with his powerful, kicking serve.

But Federer started finding his range and rallied in the third set and the momentum, already shifting toward him as Berdych's errors mounted, really shifted his way at the start of the fourth set.

Berdych recovered from double breakpoint to deuce, and Federer got another breakpoint on a close line call. Berdych wanted to challenge, but no replay was available due to a technical glitch, so the call stood. Berdych argued with the chair umpire to no avail with the crowd breaking out in jeers, then netted a forehand to fall behind for the only break of the set.

Federer led 4-0 in the fifth but, serving at 5-2, nervously squandered double match point then double-faulted to give Berdych a break chance.

He forced deuce, fired back-to-back aces — the last was No. 20 for the match — then leapt in the air with a big "Yes!"

"I enjoy those kind of fights. It doesn't happen all the time. It's always special," Federer said. "I hope it's a good omen. I feel like I could play a couple more sets, so that's a good sign."

Federer has won 13 Grand Slam singles titles, one short of Pete Sampras' record.

Federer will face No. 8 Juan Martin del Potro of Argentina, a 5-7, 6-4, 6-4, 6-2 winner over No. 19 Marin Cilic of Croatia.

The last time he rallied from 0-2 to win in five was against Rafael Nadal at Miami in 2005.

Federer, who held the No. 1 ranking for 237 consecutive weeks until losing it to Nadal last August, rarely has needed to come back from two sets.

He has done it twice in majors, against Armenia's Sargis Sargsian in the second round at the 2001 French Open and Dutchman Peter Wessels at the 2000 U.S. Open.

Federer beat Berdych in the corresponding round here last year — after he'd been pushed to 10-8 in the fifth set against Serbia's Janko Tipsarevic. He lost to another Serb, Novak Djokovic, in the semifinals.

Djokovic, who went on to win his first major by beating Jo-Wilfried Tsonga in last year's final, was playing 2006 runner-up Marcos Baghdatis in Sunday's night match.

The winner there will play seventh-seeded Andy Roddick, who ousted No. 21 Tommy Robredo 7-5, 6-1, 6-3.

Safina, who was down 5-3 and 40-15 with Cornet serving for the match, rallied to win 6-2, 2-6, 7-5 to reach the Australian Open quarterfinals here for the first time.

"I am so lucky that I'm in the quarterfinals, she was one point away," said Safina, who had eight double faults and 52 unforced errors. "My heart is still pumping so hard."

She'll next play 187th-ranked Jelena Dokic, a 2000 Wimbledon semifinalist with a career-high No. 4 ranking who is in her first Grand Slam event in three years. The local favorite beat Alisa Kleybanova 7-5, 5-7, 8-6. Kleybanova upset 2008 runner-up Ana Ivanovic in the previous round.

Bartoli was the aggressor in a 6-1, 6-4 win over Jankovic that wasn't entirely unexpected.

"Yeah, it's obviously disappointing. Nobody likes to lose," Jankovic said. "Today was a tough day for me.

"I had a slow start. I let my opponent completely come on top of me and play her game. I gave her a lot of confidence."

The 23-year-old Serb remains without a Grand Slam singles title and could also be without the No. 1 ranking in another week. If Safina wins, she'll top the rankings after the season's first major.

"It doesn't matter because it's just the beginning of the year, and there is many more tournaments to play," Jankovic said. "Maybe it will change, the No. 1 ranking, but it's not important what you do now, it's the whole year ahead of us."

Bartoli had not been past the second round in seven previous trips to Melbourne Park, but was 3-3 in head-to-heads including a quarterfinal win at Wimbledon two years ago.

She next plays No. 7 Vera Zvonareva, who beat No. 10 Nadia Petrova 7-5, 6-4 in an all-Russia match.

"I knew I could beat Jelena on a good day, it was just a matter of executing it, you know, play the right shot at the right time," Bartoli said. "But I was not overwhelmed by the situation, and I just went for my shot and everything went in."