The pair met again in Sharapova's next event in Beijing, with the five-time major champion taking the honours on that occasion in a match decided by a third-set tiebreak.
Federer entered the Australian Open previous year under similar circumstances, coming off an extended break for a knee injury, and went on to win the title. The German 21st seed needed only 64 minutes to beat the unseeded Russian 6-1, 6-3 to reach the last 16.
There were 11 service breaks and two medical timeouts - for Davis to get treatment on both feet - before Halep converted on her first match point.
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.
I learnt a lot from the last 24 months, I had a great 2016, a year ago was a little tougher.
Sharapova, playing only her second grand slam since returning from her doping suspension, took it on the chin. She then played only one match after the U.S. Open before shutting down her season early to let the wrist heal.
The Swiss star beat the Frenchman 6-2, 7-5, 6-4 in just under two hours in a night match on Rod Laver Arena.
Kerber is on a 12-match winning streak after winning four matches at the Hopman Cup and five while winning the Sydney International.
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Kerber said: "Everyone who knows me knows I always come back".
Simona Halep fended off a gutsy performance by Lauren Davis of the United States in an epic third round encounter at the Australian Open on Saturday.
Also advancing were No. 8 Caroline Garcia and No. 26 Agnieszka Radwanska, who next plays Hsieh. I mean, you know, I know that I have to play my best tennis again.
"It's a different voice", Kerber said.
As the thermometer headed towards an energy-sapping 40C and reports of 69 degrees being measured on the court surface, Djokovic and his opponent Gael Monfils took to a sun-baked Rod Laver Arena for their second-round clash. The former world No 1 had to drop out of the year's first Slam to go for a hip surgery.
Maria Sharapova, the 2008 Australian Open victor, hurried through the first set on Rod Laver Arena in 23 minutes before beating No. 14-seeded Anastasija Sevastova 6-1, 7-6 (4).
"I just feel that my muscles are gone". Dabrowski and partner Mate Pavic of Croatia defeated Australians Alex Bolt and Lizette Cabrera 6-3, 7-5.