Sharapova was banned for after testing positive for the drug meldonium here in 2016, when she reached the quarterfinals, and finished a year ago ranked No 60.
No 9 Johanna Konta beat Madison Brengle 6-3, 6-1 and will meet another American, Bernarda Pera in the second round.
"I cherish these moments".
It was sweet revenge for the Russian after the Latvian number 14 seed knocked her out of last year's US Open.
"Maybe I should have just approached these kind of points with a little bit more of intensity, a little bit more of aggressivity, but I haven't".
Former world number 2 Agnieszka Radwanska also made it through after losing the first set to Ukraine's Lesia Tsurenko.
"I was putting a lot of hours on the court in the last couple weeks, and I played a lot of practice sets, and I had only one match leading up to this tournament in Kooyong".
Her 6-3, 6-4 first-round victory over Paraguay's Veronica Cepede Royg on Tuesday will see her writing a cheque for $700 already - she served seven aces. "Yeah, it's great to be back".
The first-round upsets included Venus Williams, U.S. Open champion Sloane Stephens and CoCo Vandeweghe, a semifinalist here and at the U.S. Open past year.
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But he looked in good fettle as he worked his way into the second round where he will play Frenchman Gael Monfils.
Several other players - including Kevin Anderson, the South African who works with Djokovic on the ATP player council - have suggested that his main motivation is to help lower-ranked players, especially those around the No 150 or 200 mark.
While last year's victor and second seed of the tournament, Roger Federer, also blasted his way to a straight sets victory over Slovenian Aljaz Bedene, before getting an on-court visit from a Hollywood superstar. While the French tennis star is yet to take down Djokovic, the Serbian is attempting a return from injury as we speak.
But it was no doubt a reaffirming afternoon for one of the true champions, who was still debating whether he was healthy enough to play in this major tournament when the new year began and he had not played a genuine match since last July at Wimbledon. Federer won the Round of 128 matchup 6-3, 6-4, 6-3.
The tall tattooed Czech, who made the quarter-final in Australia previous year, was largely untroubled and is looking for a deep run at the tournament. Aiava gave her a real fight but just seemed to run out of steam.
Croatia's Mirjana Lucic-Baroni, the 28th seed and 2017 semi-finalist, was defeated 6-3 6-1 by Aliaksandra Sasnovich.
She can't wait for her next match on Thursday even though temperatures are forecast to hit 40 Celsius (104 Fahrenheit) later in the week.