Later, Caroline Wozniacki started her first major as the No. 1-ranked woman with a 6-3, 6-4 victory over Argentina's Gisela Dulko.
It was the 20-year-old Wozniacki's first win of the year, following a straight-sets loss to Slovakia's Dominika Cibulkova last week in the Sydney International and exhibition losses to No. 2 Vera Zvonareva and Kim Clijsters.
Wozniacki didn't face a break point in the first set and converted her only chance. Dulko, the top-ranked doubles player, tested Wozniacki in the second set and pulled level at 4-4 with a service break, but the Danish player broke back immediately and served it out on her second match point after a double-fault on her first.
Sharapova, the former top-ranked player who missed the 2009 Australian Open because of a shoulder injury and was ousted in the first round last year by fellow Russian Maria Kirilenko, struggled with her serve and was inconsistent in the second set. After losing the opening service game at love, Sharapova won seven consecutive games to take a 6-1, 1-0 lead.
The 33-year-old Tamarine rallied and had a game point on serve for a 4-1 lead, but Sharapova broke back and regained momentum, winning the last five games.
Even when winning, Sharapova had trouble finding range with her serve. She had 10 double-faults and five aces.
Nerves had a role in that.
"I knew I had an early exit last year and didn't want that to happen this year," she said.
French Open champion Francesca Schiavone had a couple of stutters before advancing with a 6-7 (4), 6-2, 6-4 victory over Arantxa Parra Santonja of Spain.
The sixth-seeded Schiavone had a chance to serve for the match at 5-3 in the third but was broken. The Italian player recovered quickly, breaking Parra Santonja's service in the next game to take the match.
In other women's matches, No. 20 Kaia Kanepi of Estona beat Slovakia's Magdalena Rybarikova 2-6, 6-4, 6-3 and No. 29 Dominika Cibulkova of Slovakia advanced 6-2, 6-7 (4), 6-4 over Germany's Angelique Kerber.
No. 18 Sam Querrey was the first of the men's seeded players eliminated, losing 5-7, 6-2, 3-6, 6-1, 8-6 to Poland's Lukasz Kubot, while No. 12 Gael Monfils rallied to beat former world junior champion Thiemo De Bakker.