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Playing her first match since losing to Elena Rybakina in the semi-finals of the Australian Open, Azarenka dispatched outsider Oz 6-1 6-1.
Azarenka, a two-time champion in Doha, only needed an hour and seven minutes to book a meeting with Belinda Bencic or Viktoriya Tomova.
The Belarusian broke twice in the first set and four times in the second, failing to hold just the once in a commanding display.
Eighth seed Veronika Kudermetova battled her way past Barbora Krejcikova, winning 6-4 3-6 7-6 (7-5).
Karolina Muchov secured an impressive 6-2 6-2 win over Martina Trevisan in the opening first-round match of the day.