Wozniacki, who finished back-to-back years at No. 1 in the rankings in 2010 and `11, has never won a major and is determined to make up for a first-round exit at the Australian Open last year.
Puig fought back to win the second set and force a decider but the Rio champion eventually succumbed after 2 hours and 10 minutes.
Third-seeded Dominika Cibulkova, last year’s WTA Finals champion and a finalist at the Australian Open in 2014, opened in Sydney with a 6-2, 6-0 win over Laura Siegemund, advancing along with No. 6-seeded Johanna Konta and No. 9 Roberta Vinci.
Americans Christina McHale and CoCo Vandeweghe had wins over seeded players, with McHale beating No. 4 Kateryna Bondarenko 4-6, 7-5, 6-2 and Vandeweghe leading 6-2, 4-0 when No. 8 Elena Vesnina retired from their match.
Australian hope Sam Stosur, the 2011 U.S. Open champion, had another first-round defeat, losing 6-3, 6-1 to Anastasia Pavlyuchenkova in 63 minutes.
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