Pegula, whose billionaire parents own the Bills, was in ruthless form as she won 6-0, 6-1 against 161st-ranked Romanian Jaqueline Cristian.
She then drew a heart on a TV camera and wrote "Go Bills #3" in a tribute to Damar Hamlin, the Bills player who suffered a cardiac arrest on the field earlier this month.
"I woke up around 7:00 am and got to basically watch most of the second half," she said of the Bills, who overcame the Miami Dolphins 34-31 in a tense encounter.
"Then the game finished before I started my warm-up, there wasn't really many people out here yet, but I was here watching.
"Yeah, it was fun obviously for them to get that win before I went on court. It wouldn't have really affected me, I don't think, but I would have just been annoyed if they had lost."
Pegula took just 59 minutes to oust Cristian, serving an ace on match point as she overwhelmed her 24-year-old opponent and said she had been pleased to open proceedings on Margaret Court Arena.
"I was really happy I was first on today," said Pegula.
"If I'm going to be out first round, I would rather know first match than not. I would hate to have to wait around till the last match on Tuesday."
Pegula was in fine form for the victorious USA team at the recent United Cup in Sydney, where she beat world number one Iga Swiatek in a dominant display.
"It definitely gives me a lot of confidence, winning matches like that," she said.
"Knowing I'm playing really focused every single point and not letting any kind of points or games go to waste, I think that helps your game a lot."
Pegula will play Aliaksandra Sasnovich of Belarus in the second round.
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