The third-seeded Dane broke Van Uytvanck once in each set and kept her unforced errors down to win the baseline battle in an hour and 33 minutes in the first match of the evening session at the Rod Laver Arena.
The 24-year-old Van Uytvanck, ranked 52, troubled Wozniacki with some well-disguised drop shots but did not have enough to register her maiden win at Melbourne Park in her fifth appearance in both singles and doubles.
Wozniacki, who is battling rheumatoid arthritis, sealed the match with a forehand winner on her third matchpoint and will next meet Sweden's Johanna Larsson, who progressed after Vera Lapko of Belarus retired while trailing 7-6(5) 3-0. (Reporting by Sudipto Ganguly; editing by Amlan Chakraborty)
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