Now seeded 14th, Djokovic needed four match points in an eight-minute last game before clinching the win against Monfils, who needed a medical timeout for heat stress and said he had trouble breathing.
This was Sharapova's first appearance at the Australian Open since 2016, when she tested positive for meldonium and later was handed a 15-month ban.
Kerber celebrated her 30th birthday with a 6-4 6-1 win over Donna Vekic as she made it an impressive 11 wins in a row to start the season. Sometimes that's all it takes, ' said Sharapova, slightly skimming over such a comprehensive outcome.
In what was the longest game of the match, Hsieh prevailed with an array of fantastic winners as both players were putting up a good show for the Margaret Court Arena crowd. "Today was not enough (but). looking at the overall picture, there's a lot to build from".
Former American greats Chris Evert and Tracy Austin took to twitter to praise Simona Halep and Lauren Davis for producing a three-set thriller on Rod Laver Arena.
The third set took 2 hours, 22 minutes.
It is fair to point out that she did have a brutal draw, facing her US Open conqueror Anastasija Sevastova in the second round, and then one of the recent form players of the tour in the third.
She saved one match point in the ninth game on her serve before Hsieh served out the match in the next, clinching it with a winning backhand to the corner.More news: Jacinda Ardern baby gives New Zealand's opposition sleepless nights
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"I played much better than I expected because of the foot".
"I look forward to these matches".
"He's always been around me and supported me and was fantastic", she said of McNamee's influence. "My ankle is, I don't know how it is because I don't feel it anymore!"
The older Chan and Hlavackova, the No. 1 seeds in the women's doubles, advanced to the third round with a 6-0, 7-5 win over Oksana Kalashnikova of Georgia and Varvara Lepchenko of the United States.
Italian Fabio Fognini has equalled his best run at the Australian Open with a 3-6 6-2 6-1 4-6 6-3 third-round victory over France's Julien Benneteau.
The world No 3, who had been in with a chance of returning to the top of the world rankings at the end of the tournament, was beaten 7-6, 6-4 as Hsieh outwitted and outmanoeuvred the Wimbledon champion. Sixth-seeded Karolina Pliskova beat No. 29 Lucie Safarova 7-6 (6), 7-5.
Taiwanese veteran Hsieh Su-wei reached the fourth round of a Grand Slam for only the second time yesterday, when she rolled past Agnieszka Radwanska at the Australian Open.
Six-time Australian Open champion Djokovic continued his comeback from six months out with an injured right elbow, beating No. 21 Albert Ramos-Vinolas 6-2, 6-3, 6-3.