Last week, Djokovic lost in straight sets to Ernests Gulbis of Latvia in the first round of the Brisbane International. He said he struggled to find his rhythm with a new racket in that match and wasn't overly concerned about the loss.
On Wednesday, he backed up that claim in searing heat at the Olympic Park Tennis Centre. The temperature reached 98 degrees - conditions that should prepare Djokovic for his title defense at the Australian Open beginning Monday in Melbourne.
"I was more or less happy with my consistency throughout the match,'' he said. "I wasn't really having a lot of ups and downs.''
Top-seeded Serena Williams saved two match points in the 12th game of the final set before beating Caroline Wozniacki of Denmark 6-7 (5), 6-3, 7-6 (3).
Williams had to save four match points in her first-round match against Samantha Stosur of Australia, and had a straight-sets win in the second round before dueling with Wozniacki for 2 hours, 40 minutes at Ken Rosewall Arena in the quarterfinals.
It was the eighth time in her career that Williams has come from a match point down to win. On six of those occasions she has gone on to win the tournament.
"It definitely was lucky today,'' Williams said. "I had a lot of errors on easy shots. I really should have closed it off in two sets. I'm not really happy with the way I played today.''
No. 2-seeded Gilles Simon was beaten 6-4, 6-4 by French compatriot Richard Gasquet while another Frenchman, third-seeded Jo-Wilfried Tsonga, downed Italy's Simone Bolelli of Italy 6-4, 6-1.
Argentina's David Nalbandian also swept into the quarterfinals with a 6-1, 6-3 win Michael Llodra of France.
Jeremy Chardy was the third Frenchman into the last eight, upsetting fifth-seeded Igor Andreev of Russia 6-4, 4-6, 6-4 while seventh-seeded Spaniard Tommy Robredo was thrashed 6-2, 6-1 by Croatia's Mario Ancic.
Djokovic was cheered on by a large section of Serbian fans dressed in red and waving national flags. Serb and Croatian fans had a violent confrontation during the 2007 Australian Open.
Australia's Lleyton Hewitt and Finland's Jarkko Nieminen also won Wednesday to reach the quarterfinals.
Top-seeded Serena Williams of the United States was scheduled to play Caroline Wozniacki of Denmark in a quarterfinal match later at the joint ATP-WTA tournament.
Second-seeded Dinara Safina of Russia joins Williams in the semifinals with a 6-3, 6-4 win over France's Alize Cornet. Cornet saved four match points in the final game before Safina closed the match out.
But Safina called her play "a disaster'' and said Cornet could have won the match if she were a little more experienced.
"She gave me the match,'' Safina said after trailing 4-1 in the second set. "It's not the way I want to win the match. I want to win it by myself, not that the girl loses to me. I don't like the way I'm playing. Just totally bad.''
Safina next faces Japan's Ai Sugiyama, who made it to the semifinals when former U.S. Open champion and fifth-seeded Svetlana Kuznetsova of Russia withdrew with an abdominal strain.
Third-seeded Elena Dementieva of Russia beat No. 6 Agnieszka Radwanska of Poland 6-2, 5-7, 6-4 in another quarterfinal and will face Williams in the semis.
Dinara Safina easily wins opening match at Sydney
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