Last week, Djokovic lost in straight sets to Ernests Gulbis of Latvia in the first round of the Brisbane International. Then, he said he was struggling to find his rhythm with a new racket and wasn't overly concerned about the loss.
On Wednesday, he backed up that claim with a strong display against Mathieu in searing heat at the Olympic Park Tennis Centre. Those temperatures should help set him up for his defense at the Australian Open beginning Monday in Melbourne, where, about 800 kilometers (500 miles) to the south, it tends to get just as equally hot and steamy.
The Serbian's serve still wasn't perfect Wednesday with the new racket, but he was helped by Mathieu, who was only able to take advantage of three of his seven break-point chances.
Djokovic said he was not 100 percent comfortable yet with the new racket, but was pleased with his serve and his game Wednesday.
"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.''
Djokovic was cheered on by a large and well-behaved section of Serbian fans dressed in red and waving national flags. During the match, the Serbian player sometimes faced that section and raised his arms in appreciation, drawing more cheers.
He will play Croatian Mario Ancic in the quarterfinals, who Djokovic called a "great talent'' and a good friend, and acknowledged it would be a tough match.
Djokovic received a first-round bye along with three other top seeds, and two of them advanced along with him on Wednesday to the quarterfinals - No. 3 Jo-Wilfried Tsonga of France, whom Djokovic beat in the Australian Open final last year, No. 4 David Nalbandian of Argentina and local favorite Lleyton Hewitt.
Tsonga beat Simone Bolelli of Italy 6-4, 6-1, although Tsonga was troubled by a back complaint at times, and twice received treatment during his match on Ken Rosewall Arena. Nalbandian beat Michael Llodra of France 6-1, 6-3. Hewitt beat Serbian Janko Tipsarevic 7-5, 6-4 and Ancic beat seventh-seeded Tommy Robredo of Spain 6-2, 6-1.
Second-seeded Gilles Simon of France played countryman Richard Gasquet later Wednesday.
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 advanced with a 6-3, 6-4 win over Frenchwoman Alize Cornet. Cornet saved four match points in the final game before Safina, who was serving, 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 of the French player, who was up 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.''
She said she would have to turn her game around and play more aggressively to beat her next opponent, veteran Ai Sugiyama of Japan. Sugiyama made it to the semifinals without taking to the court, receiving a walkover when former U.S. Open champion and fifth-seeded Svetlana Kuznetsova of Russia withdrew with an abdominal strain.
Kuznetsova said the injury put too much during serves and backhands, and that her physiotherapist had advised a few days of rest before she tests herself again in Melbourne.
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