Sharapova, a five-time Grand Slam title winner, received a wild card for the main draw at Melbourne Park after her year-end ranking slipped to 136 in 2019, a season interrupted by injuries. The 2008 Australian Open winner reached the fourth round here last year, missed the French Open and lost in the first rounds at Wimbledon and the US Open.
The 32-year-old Russian has had a series of right shoulder injuries and served a 15-month suspension for testing positive for meldonium. Since her return from the suspension, her best showing at a major has been the quarterfinals at the 2018 French Open.
She wasn't making any excuses after her loss Tuesday.
"I mean, I think I'm not the only one -- I can speak about my struggles and the things that I've gone through with my shoulder, but it's not really in my character to," Sharapova said.
Although Sharapova's profile means she still gets a spot on center court, it was only Vekic's second time on Rod Laver Arena.
"I always enjoy the big stages," Vekic said. "I'm happy to leave with a win this time."
Pliskova, who lost to eventual champion Naomi Osaka in the semifinals here last year, started the season with a title in Brisbane.
"It's a new beginning here," Pliskova said. "The weeks before, nobody really counts, and nobody remembers. But I had some very good matches."
Also Tuesday, two-time Grand Slam title winner Garbine Muguruza appeared to be on the way to a third consecutive first-round exit at a major when she dropped the opening set at love against American qualifier Shelby Rogers.
And then Muguruza turned everything around in remarkable fashion, grabbing 12 of the last 13 games to beat Rogers 0-6, 6-1, 6-0.
Muguruza won the French Open in 2016 and Wimbledon in 2017 and spent time at No. 1 in the rankings. But she's unseeded at Melbourne Park and started as poorly as possible.
So what was she thinking late in that first set?
Muguruza recalled: "I said to myself, 'Hey, you're here, you're on the court, you're playing [at the] Australian Open. It's a special moment, so just hang in there and keep fighting.'"
Cici Bellis has won a Grand Slam match for the first time in nearly three years after having a series of operations.
The 20-year-old Californian, once ranked as high as 35th, beat Tatjana Maria of Germany 6-0, 6-2.
Bellis was sidelined for about 20 months because she needed surgery on her right wrist or arm a total of four times. Her last victory at a major tournament came when she got to the French Open's third round in 2017.
Two-time Grand Slam titlist Svetlana Kuznetsova also ended her own drought, coming away with her first win at a major since 2017.
Halep has had four first-round exits at Melbourne Park, but not since she reached the final here in 2018 -- having saved match points in third round and the semifinals.
She won the French Open in 2018 and Wimbledon last year, and is seeded fourth in Australia.
Halep hurt her right wrist when she stumbled on the court in the 10th game, and was broken in the 11th game. But she broke back immediately as Brady served for the set, and then dominated from midway through the tiebreaker.
Johanna Konta, the 2016 Australian Open semifinalist, lost her first-round match to Ons Jabeur 6-4, 6-2 on Tuesday. It was only her second match since she lost in the quarterfinals of last year's US Open, due to a tendinitis-related problem in her right knee.
Konta lost in the first round at the Brisbane International and then withdrew from the Adelaide International in an attempt to manage her injury. Even before she left for Australia, the British No. 1 told officials that she wouldn't play Fed Cup this year.
The 12th-seeded Konta appeared to be moving without issue Tuesday but was outclassed by the 25-year-old Tunisian player who beat her the previous time the two played, last year at Eastbourne. Jabeur broke Konta to win the first set. The British player replied with her only break of the match to open the second, but Jabeur dominated the rest of the way.
"I think ultimately the main thing was to start playing again, and I am," she said. "And how I physically felt out there is obviously a massive tick for me compared to where I was in September of last year. Before Brisbane, I had been out for almost 4½ months. So it's been quite a bit of time, not far off getting a protected ranking."
Jabeur said her goal this year is to make it into the top 20 -- she's currently 78th -- and to inspire other African Arab players to pick up the sport. "It would be nice to see more of us out here on tour," she said.
After torrential rain hit Melbourne Park on Day 1, organizers had to move dozens of events to Tuesday, including the Konta-Jabeur match.
The Associated Press contributed to this report.