Djokovic took 25 minutes to win the first set against No. 28-seeded Andreas Seppi but needed nearly an hour in the next two, saving two set points in the tiebreaker before winning 6-1, 7-5, 7-6 (6) win on Margaret Court Arena.
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Williams won the first set of her Rod Laver Arena match in 22 minutes and was helped by four double-faults by Kasatkina.
Returning refreshed after a lengthy bathroom break, Sharapova broke for a 2-0 third-set lead as Davis bounced her Wilson racquet off the court in frustration over her errant serve.
Sharapova notched up her 600 career win, but was made to work hard at it, after being taken to three sets by USA’s Lauren Davis. In the crucial eleventh game, the Russian had her chances but the American had an answer to everything the five-time Grand Slam champion threw at her, eventually holding for 6-5.
Sharapova, a full foot taller than the 22-year-old, had been in scintillating form so far, dropping just seven games in her opening two matches.
Sharapova’s first seed is the big hitting Anastasia Pavlyuchenkova, and then comes Svetlana Kuznetsova or Belinda Bencic.
He lost in the third round in his first two trips to Melbourne Park in 2000 and ’01 and again last year – in between he won the title four times and lost one final during a run of reaching the semifinals or better in 11 straight years.
Meanwhile, Williams faces Su-Wei Hsieh of Taipei in the second round after dismissing Italy’s Camila Giorgi 6-4 7-5 in the opening round. But Dimitrov levelled the match at a set apiece with his aggressive play, paying dividends in the second set.
“Oh, wow, I’ve won 600 matches?” she said with surprise.
“I think it’s 40 years on the tennis tour that doesn’t excite me, you know”, he said with a laugh.
“I was quite happy I was able to step it up in the third set”.
AND ELSEWHERE: Qualifier Zhang Shuai, who beat No. 2-seeded Simon Halep in the first round, plays Varvara Lepchenko.
“In the first set I was sore but after treatment I felt better”, he said.
Sharapova said she had been working on mixing up her game, which some pundits have seen as too one-dimensional to beat top seed Williams, who has long dominated the Russian.
Nigel Willerton, head of the Tennis Integrity Unit which was formed in 2008 as a joint initiative of the International Tennis Federation, the ATP, the WTA and the Grand Slam Board, says “it would be unprofessional for me to comment on if any players here are being monitored”. “I’m just glad I got through”.
“I don’t have a chat in the mirror, I think I get fined for that”, Sharapova said courtside of her trip to the locker-room.
The seventh-seeded Nishikori, who reached the quarterfinals previous year, beat Philipp Kohlschreiber 6-4, 6-3, 6-3 without facing a break point Monday.
Andy Murray, Stan Wawrinka and Victoria Azarenka aim to continue their quests for a third Grand Slam singles title when they play their third-round matches Saturday at the Australian Open.
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Djokovic lost to Santoro 6-3, 6-2 in the second round of the Paris Masters indoor tournament in October 2007.
