The 18-year-old won 6-3 6-4 on Sunday to book a second-round clash with the former world No.1.
"The sunglasses help because you can't really see all my face. But I was pretty nervous," she laughed.
Joint climbed 655 places to No.116 this year thanks to two International Tennis Federation titles, a WTA 125 final and a win over Laura Siegemund to reach the second round at the US Open.
Beaten by Madison Keys at Flushing Meadows, the teenager said she was ready for another high-profile test against Azarenka, who had a first-round bye.
Joint's win will help continue her rapid rise up the WTA rankings. (Jono Searle/AAP PHOTOS)
"I'm really excited to play her," Joint said of her next task against the 10th seed and two-time Brisbane event winner.
"I'll think back to my Madison Keys match; that was a great experience. I hope I can play well again.
"There was a lot of things that I saw that I needed to improve in my own game to be competitive with those sorts of players. So I'll see how that goes."
In other matches, Renata Zarazua beat Viktoriya Tomova 6-0 6-3 to set up a clash with current world No.1 Aryna Sabalenka in the second round.
Elina Avanesyan beat Rebecca Sramkova 1-6 6-2 6-2 while Ashlyn Krueger and Suzan Lamens also won.
Ash Barty and Pat Rafter opened the season-launching event in an exhibition mixed doubles feature.
Ash Barty, expecting her second child, made a cameo exhibition appearance in Brisbane. (Jono Searle/AAP PHOTOS)
Barty has repeatedly talked down the prospects of a return to competitive tennis and on Christmas Day announced she was expecting her second child since her sudden retirement after winning the 2022 Australian Open.
She won the first set with American talent Frances Tiafoe 6-3 before Rafter and partner Ons Jabeur retired.
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