In a hopelessly one-sided first set, the world number 48 powered home 12 winners, was successful on all six occasions she approached the net, smashed down two aces and lost just nine points.
Sharapova will face Anastasija Sevastova in the second round and, if she makes it through that, 2016 champion Angelique Kerber looms.
American woes continued with Madison Brengle sent packing by British ninth seed Johanna Konta.
Wawrinka, who had six months out after surgery on his left knee, beat Ricardas Berankis 6-3, 6-4, 2-6, 7-6 (2).
Elena Vesnina became the 10th of the top 16 women's seeds to go out by the second round, losing 7-6 (7-4) 6-2 to Japanese 20-year-old Naomi Osaka.
Meanwhile in a late evening match, World No.1 Simona Halep flirted with another early exit and suffered an ankle injury before rallying to reach the second round with a 7-6 (7-5), 6-1 victory over local teenager Destanee Aiava. "I think I have a small heatstroke for 40 minutes. even with the ice towel, the water, I think my body was super warm".
Argentinean Juan Martin del Potro fired 60 winners on his way to a 6-4 7-6 (4) 6-7 (0) 6-4 second-round victory over Karen Khachanov of Russian Federation.
The 17th-seeded Keys, the U.S. Open runner-up, advanced with a 6-1, 7-5 win over Wang Qiang and will be one of four American women who made it through the opening two days.
Djokovic, untroubled by scorching conditions at Melbourne Park, beat Frenchman Gael Monfils 4-6 6-3 6-1 6-3 in the second round, though he took aim at organisers for allowing play to continue in such heat. But now is the moment, for me personally, to play tennis, to play tennis and to try my best on court. "Really tough conditions, brutal - especially for the first hour and a half".
When both these boxes are ticked, matches on outside courts are halted and roofs closed on all three indoor-capable venues. She was also aggressive on return, which paid dividends for the Russian as she was able to break twice in the opening set before taking it 6-1.
Next up is in-form 2016 Australian Open champion Angelique Kerber, who beat Donna Vekic in two easy sets as she starts to rediscover her best again after a miserable a year ago. Her birthday gift? A blockbuster clash with 2008 victor Maria Sharapova in the next round.
Sydney-born Konta, a quarter-finalist a year ago, 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.
"I love Australia. I love the summertime".
"I was watching this tournament with a box of Kleenex next to me sick". It's hard to prepare for that in some ways, but you know when you come down here that can happen.