There were no further flashpoints on Tuesday, with Azarenka - who shapes as the most dangerous spoiler in the draw - advancing to a second-round clash with No.8 seed Caroline Wozniacki.
The Danish star was made to work hard in the first set by American Taylor Townsend before lifting in the second to win 7-6 (7-1) 6-2.
"You're always a little bit nervous - it's the first grand slam of the year," said Wozniacki.
"You like to start off well."
Last year's Open runner-up Dominika Cibulkova overcame a first-set blip to beat Belgian Kirsten Flipkens 3-6 6-3 6-1.
The Slovakian is seeded 11th, having enjoyed her best year on the tour in 2014.
Australian flagbearer Samantha Stosur, the No.20 seed, crushed Romania's Monica Niculescu 6-4 6-1.
No.24 seed Garbine Muguruza from Spain beat New Zealand's Marina Erakovic 7-5 6-0.
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-AAP