After the victory, Pegula wrote on the on-court camera in celebration: "Bills you're next."
Pegula, 27, tweeted about wearing Bills' colors during her time in Melbourne earlier in the week.
"Coincidence I'm in Bills colors?" she wrote.
Coincidence I'm in Bills colors? Round 3 here in Aus 👏🏼 pic.twitter.com/uBH1AJI21X— Jessie Pegula (@JLPegula) January 19, 2022
Pegula recorded her best career major result at the 2021 Australian Open with a run to the quarterfinals before losing to eventual finalist and fellow American Jennifer Brady.
The 24th-seeded Azarenka won the title at Melbourne Park in 2012 and 2013, and she also has been the runner-up at the US Open three times, most recently in 2020. Since a quarterfinal run in Australia in 2016, Azarenka lost first-round matches last year and in 2019 and missed the hard-court tournament in 2017, 2018 and 2020.
"I always feel privileged that I'm able to have him here,'' said Azarenka, who was accompanied by her 5-year-old son when talking to reporters after the match. "These kind of moments are really priceless for me. To be able for me to share that with my son is pretty incredible.''
In other results on Day 5, eighth-seeded Paula Badosa had a 6-2, 5-7, 6-4 win over Marta Kostyuk to move into a fourth-round match against American Madison Keys, who held off Wang Qiang 4-6, 6-3, 7-6 (2).
The Associated Press contributed to this report.