With the temperatures heading towards an energy-sapping 39 Celsius (102 Fahrenheit) and ice-towels in use, the Russian drawcard worked hard to get off court early against Anastasija Sevastova.
It was the Latvian 14th seed who ended her Grand Slam comeback in the last 16 of the US Open in 2017 as she returned from a drug ban. But not this time.
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.
“You know, it was a warm day. I did my job in two sets against someone that’s been troubling in the past for me,” she said afterwards.
“So third round of the Australian Open. I think I deserve to smile out there after that victory.”
Being unseeded means she has her work cut out to reach another final, with a host of hurdles in her way.
Next up could be in-form 2016 Australian Open champion Angelique Kerber, who plays Donna Vekic later and is starting to show glimpses of her best again after a miserable last year.
Eighth seed Garcia also stayed in the title hunt, but she found it hard going against Czech teen Marketa Vondrousova who pushed her to three gruelling sets.
The Frenchwoman, who had a breakout year in 2017, winning two titles, eventually got over the line 6-7 (3/7), 6-2, 8-6 in almost two-and-a-half hours.
“My feet are burning,” she said. “But we know it’s like this in Australia — the next day it can be freezing.”
Two-time tournament semi-finalist Radwanksa, who has slid down the rankings and is only seeded 26, continued her under-the-radar progress with a three set win over Lesia Tsurenko.
She could potentially face third seed Garbine Muguruza next, who is still struggling with a right thigh problem and tests it against Taiwan’s Hsieh Su-wei.
British hope Johanna Konta is no longer in contention after she was bundled out by American “lucky loser” Bernarda Pera.
Sydney-born Konta, a quarter-finalist last year, was no match for American, who is only in the main draw after a player pulled out before the Grand Slam began, as she fell 6-4, 7-5.
– FedExpress rolls again -Among men through to the third round was Spain’s 21st seed Albert Ramos-Vinolas, who swept past American Tim Smyczek in straight sets.
Hungarian Marton Fucsovics, ranked 80, piled more misery on the United States, beating 13th seed Sam Querrey, with the American contingent in Melbourne — men and women — decimated in the early rounds.
Roger Federer rolls back into action later with the Swiss world number two headlining Rod Laver Arena in the evening.
He faces Jan-Lennard Struff, and the signs are ominous for the German.
Defending champion Federer has made at least the third round each year since his debut at Melbourne Park in 2000. In contrast, Struff has failed to get further than the second round ever, at any Grand Slam.
Twelve-time Grand Slam champion Djokovic was in fine fettle in his opening match as he returns from an elbow problem that kept him out of action for six months.
Seeded 14, his next test in the afternoon heat will be far tougher against experienced Frenchman Gael Monfils, although the Serb holds an unblemished 14-0 record.
In other matches, fourth seed Alexander Zverev plays fellow German Peter Gojowczyk and 2014 Australian Open champion Stan Wawrinka continues his comeback from a lengthy injury lay off against Tennys Sandgren.
World number one Simona Halep, who was unconvincing in her first round encounter, takes on Canadian Eugenie Bouchard. DM
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