Also out was 2011 champion Petra Kvitova, who lost 6-4, 7-5 to Russia's Anastasia Pavlyuchenkova in a season-opening tournament that has proved rough for many of the top players.
Serena Williams, however, had no such problems. She carried her relentless winning form into 2013, reaching the quarterfinals with a 6-2, 6-2 victory at night over No. 44-ranked Alize Cornet.
Williams, a 15-time major winner who is ranked No. 3, has lost only one of her last 34 competitive singles matches in a run that includes titles at Wimbledon, the London Olympics and the U.S. Open.
She was hitting winners so fiercely that Cornet didn't bother chasing most of them. One of her serves, in the fourth game of the second, was 124 mph (200 kilometres). That was faster than any of her serves last year, and she has rarely served faster anywhere.
"I just really went for it. I've hit 200 before but they never go in so I was really excited that it went in," Williams said. "I tried to be more aggressive."
Sharapova, ranked No. 2 and the French Open champion, didn't want to risk worsening a collarbone problem that flared late last month and also forced her from an exhibition in South Korea. She started hitting overheads and serves only on Monday and said it was wiser to head to Melbourne to get ready for the year's first Grand Slam tournament, which begins Jan. 14.
"I still have quite a bit of time to prepare for Australia. I'm on the right track, been training really well, so I just don't want to jeopardize what I've gained in the off-season so far," she said. "Just have to make a smart move here."
Kvitova, who won the Brisbane title five months before claiming her first Grand Slam crown at Wimbledon in 2011, didn't find any rhythm against Pavlyuchenkova. She will head to Sydney for more matches before the Australian Open.
Combined with Daniela Hantuchova's 4-6, 6-1, 7-5 win over No. 5 Sara Errani and the first-round exits of No. 7 Sam Stosur and No. 8 Caroline Wozniacki, the season-opening event featuring eight of the top 10 ranked women had already lost five of its top eight seeds before the end of the second round.
"This tournament was a really tough draw, everybody's playing," Kvitova said. "After the off-season, it's hard to be on the court against some opponents."
Williams will next meet the winner of Wednesday's match between fellow American Sloane Stephens and Sweden's Sofia Arvidsson.
She said she had a touch of insomnia after arriving in Australia, and was awake listening to the New Year's Eve fireworks on Monday but not able to join the celebrations.
Now she's hoping for a night quarterfinal.
"I don't know what time zone I'm in. I don't know if I'm in Florida or if I'm in Mauritius or if I'm in Brazil. I just don't know anymore," she said, but "I'm good when I'm awake."
If she continues her dominating run right through the Australian Open, the 31-year-old Williams has a good chance of becoming the oldest player to be ranked No. 1. Chris Evert holds that record — she was 30 years, 11 months when she last held the top ranking in 1985. She attributes her resurgence since her first-round exit at the last French Open to a feeling of invigoration.
"I just feel alive," she said. "I feel really alive."
On the men's side, local qualifier John Millman, ranked No. 199, advanced to a second-round match with Olympic and U.S. Open champion Andy Murray by beating Japan's Tatsuma Ito 6-4, 6-1.
Seventh-seeded Jurgen Melzer of Austria downed Denis Kudla of the U.S. 2-6, 6-4, 6-4, while eighth-seeded Martin Klizan of Slovakia lost 6-1, 6-2 to Denis Istomin of Uzbekistan.
Spain's Tommy Robredo advanced 6-4, 7-6 (4) over American Ryan Harrison, and Alejandro Falla of Colombia set up a second-round match with third-seeded Gilles Simon with a 6-1, 7-6 (8) win over Jesse Levine.