Sharapova was unstoppable in racing through the first set 6-1 before a battle in the second to prevail 7-6 (7/4), proving she must again be taken seriously.
But Kerber, who plummeted down the rankings last year after finishing the year before at number one, broke her serve in the first game of the match and that set the tone for what followed.
"I knew before that it will be a tough match".
He lost the first set before Monfils began badly wilting in the heat in the second and was heard at one point telling the umpire: "I'm exhausted and dizzy".
"I think I'm just very well aware that I think in this world everyone has an opinion and that no matter what you do, or no matter how you play tennis, or what you say, or how you go about your life, not everyone will like the way you do it", she said. So, you know, I feel like I transported myself into the TV this year and I'm finding myself on Rod Laver Arena competing. "Maybe not the roof because the fittest wins, and I think that is fair enough", he said.
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Sharapova, who missed last year's Australian Open while serving a 15-month ban for a failed doping test, was happy to beat the player who'd ended her run at the U.S. Open last year.
In the men's draw, Novak Djokovic kept his campaign alive despite showing his body still is not in peak condition.
But there was concern in his camp when the former world No.1 sought a medical timeout early in the second set for treatment to his lower back.
Big names Juan Martin Del Potro, Tomas Berdych and Alexander Zverev all booked their way to the next stage in 4 sets and for the first time at the Australian Open, South Korean Hyeon Chung made it to the third round with his win over Daniil Medvedev. Federer has won 16 of the 18 times he's played Gasquet.
"The matches are going to get tougher from now on", he said. "But I'm here because I'm motivated to get better at my craft".
"It's nice coming back from a set down [but] you never like being a set down to begin with", she said. "Obviously for me it's taking one match at a time". I have some incredible memories in Melbourne Park in the last decade of my career.
Djokovic exceeded expectations after six months sidelined by an elbow problem during his opening round clash against Donald Young, but his latest display was much more of a patchy performance. I thought I was very good.