Maria, though, refused to surrender despite spending much of the match well behind the baseline as she broke to love in the fourth game for a surprising 3-1 advantage.
This was Sharapova's first time back since failing a doping test at the 2016 event, and her second Grand Slam since the ensuing suspension ended.
Sharapova could next play 14th-seeded Anastasija Sevastova of Latvia, who beat the Russian at last year's U.S. Open.
Wimbledon was also considered unlikely to offer her a wild card, although the All England Club leadership that runs the event never had to make that decision because she withdrew from the entire grass-court season a year ago with an injury.
The former champion defeated German Tatjana Maria in straight sets.
Bautista Agut lost to fellow Spaniard Fernando Verdasco, a semifinalist here in 2009, and Raonic lost 6-7 (5), 7-5, 6-4, 7-6 (4) to Lukas Lacko in the opening match on Show Court 2. Just like everyone in the draw we know it is going to get tougher in the next few rounds'.
She next plays ninth-seeded Johanna Konta of Britain, a victor over another American on Tuesday, Madison Brengle.
Jo Konta has been tipped as a contender for the Australian Open title after linking up with Maria Sharapova's former coach.
Maria Sharapova safely through after win over Maria Tatjana
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.
"They both want it really bad".
"I look forward to the heat, I love it", she said.
Konta beat Madison Brengle 6-3, 6-1, the 10th loss in 11 first-round matches for American women.
Former world number one Pliskova was among those to move smoothly into the second round, with a steady 6-3, 6-4 win over Veronica Cepede Royg.
Sixth seed Karolina Pliskova and eighth seed Caroline Garcia also progressed, in contrast to the other side of the draw that saw Venus Williams, Sloane Stephens and Coco Vandeweghe crash out on Monday.
That appeared to knock Sharapova off her stride, but only momentarily, surviving a wobble by reeling off four successive games to reach the next round, sealing her win with an ace.
Also set to play their first-round matches are six-time champion Novak Djokovic, Maria Sharapova, who is playing at Melbourne Park for the first time since testing positive for the banned drug meldonium here, and the Canadian pair of Milos Raonic and Eugenie Bouchard.More news: Conor McGregor In Danger Of Losing UFC Title
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