Playing against Santiago Giraldo, ranked 55 places behind him, Djokovic made four straight unforced errors in the fifth game to hand the Colombian the first service break of the match. But Djokovic quickly broke Giraldo to love in the next game and went on to win the next seven on his way to a 6-3, 6-2, 6-1 victory at Melbourne Park, playing much more like the man who won three Grand Slam singles titles and 41 matches in a row last year.

“I maybe started a little too defensive because he was hitting the ball very strong,” Djokovic said. “But then after, it was the other way around.”

A title this month would put him in select company. Only four players— Laver, Pete Sampras, Roger Federer and Rafael Nadal—have won three straight Grand Slam singles tournaments, and Djokovic could join them following his wins at last year’s Wimbledon and U.S. Open.

Second-seeded Nadal and third-seeded Federer, who are in the other half of the draw here, play back-to-back matches at Rod Laver Arena on Friday.

Fourth-seeded Andy Murray, who lost to Djokovic in the final here last year, also advanced Thursday, beating Edouard Roger-Vasselin of France 6-1, 6-4, 6-4. Later, players who could give both Djokovic and Murray some competition in their half of the draw—former finalist Lleyton Hewitt and American Andy Roddick— had a night match at Rod Laver Arena.

Murray is playing his first Grand Slam tournament since hiring eight-time major champion Ivan Lendl as his coach.

“It’s been good, he’s obviously one of the greatest players ever,” Murray said. “He’s got so much experience and he’s very funny guy. You wouldn’t probably expect it by the way he was on the court, similar to myself.”

Earlier, five-time Australian Open champion Serena Williams notched her 500th career singles victory when she beat Barbora Zahlavova Strycova 6-0, 6-4 to advance to the third round. The left ankle she badly sprained two weeks ago wasn’t an issue.

“It’s totally fine. It was my good ankle, so I’m good,” she said.

Williams won the Australian Open in 2009 and 2010, but didn’t defend her title in 2011 because she was injured.

Her older sister, Venus, has a win-loss record of 589-147, but is missing the Australian Open to recover from illness.

“I knew I had to get there too, because I do everything she does,” said Williams, “It’s great, it’s like the ultimate.”

Not quite. Martina Navratilova had a career record 1,442-219, and Chris Evert retired with a 1,309-146 win-loss mark.

“I never will get there either, but it’s really cool,” Williams said. “Five hundred is a lot of matches to play, let alone to win.”

With top-seeded Caroline Wozniacki on an off-day, No. 2 Petra Kvitova moved into the third round with a 6-2, 2-6, 6-4 win over Carla Suarez Navarro. Kvitova, who lost in the first round at the U.S. Open in the first major after winning Wimbledon, was down a service break in the third before recovering to beat the Spaniard.

“In the beginning it was OK, but I made many, many, many mistakes,” Kvitova said of her 48 unforced errors. “It’s part of my game but it’s too many. It was very tough to get back in the third set.”

Maria Sharapova, one of the three former champions in the women’s draw, reached the third round after just two hours on court in two matches. The 2008 champion had a 6-0, 6-1 second-round win over U.S. qualifier Jamie Hampton in 64 minutes

Sharapova did not play in any warmup events and spent nearly two weeks in Melbourne ahead of the season’s first major while she rested an injured left ankle.

“It was more about getting my feet going … worrying about myself,” Sharapova said. “Yeah, started my preparations in the offseason a little late, took a bit of extra time in practice instead of rushing into a tournament.”

She’ll meet No. 30 Angelique Kerber, who beat Canada’s Stephanie Dubois 7-5, 6-1.

Seventh-seeded Vera Zvonareva, a two-time semifinalist at Melbourne Park, had a 6-1, 7-6 (3) over Lucie Hradecka. No. 21 Ana Ivanovic also advanced, beating Dutch player Michaella Krajicek 6-2, 6-3.

Ninth-seeded Marion Bartoli beat local hope and former quarterfinalist Jelena Dokic 6-3, 6-3 and No. 27 Maria Kirilenko of Russia topped Aleksandra Wozniak of Canada 6-4, 1-6, 6-2. Dokic double-faulted on break point in the seventh game of the second set, then Bartoli closed with ace.

Three seeded players were beaten: No. 23 Roberta Vinci lost to China’s Zheng Jie, No. 29 Nadia Petrova fell to Sara Errani and No. 25 Kaia Kanepi lost to Ekaterina Makarova.

In the men’s draw, sixth-seeded Jo-Wilfried Tsonga, who lost the 2008 final to Djokovic, advanced 7-5, 6-4, 6-4 over Ricardo Mello of Brazil, while No. 5 David Ferrer struggled early against American Ryan Sweeting before coming back to win 6-7 (4), 6-2, 3-6, 6-2, 6-3

No. 9 Janko Tipsarevic, No. 23 Milos Raonic of Canada, No. 24 Kei Nishikori of Japan and No. 27 Juan Ignacio Chela also progressed. Frenchman Michael Llodra beat No. 32 Alex Bogomolov Jr. 6-1, 6-3, 4-6, 5-7, 6-4 and Portugal’s Frederico Gil beat No. 26 Marcel Granollers in four sets.

Djokovic, for all his success at Rod Laver Arena—his first Grand Slam title in 2008 and then again last year—doesn’t have any feeling of superiority on the tournament’s center court.

“I don’t think anybody is invincible,” he said. “It’s a matter of the confidence that you have, self-belief on the court, qualities as a player, being out there physically, mentally fit, being able to perform your best on a day-to-day basis.

“It is true, from one side, that when I step in there I feel that I belong there, that I know what to do. I feel more confident maybe than the other courts around the world.”

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