The 39-year-old, playing an unparallelled 100th match at the tournament, looked sharp and hit 16 winners against Germany’s Laura Siegemund in the 6-1, 6-1 romp in 56 minutes.
As she completed her first-round victory, fellow American Brady was lifting his seventh Super Bowl title having spearheaded the Tampa Bay Buccaneers to an upset 31-9 victory over the Kansas City Chiefs.
“It’s unbelievable… it’s unreal,” Williams said of the 43-year-old Brady, who collected his fourth Super Bowl MVP in his first season since leaving New England Patriots.
“I just was watching as much as I could.
“You can’t say it was the system he was at formerly. It’s definitely Tom Brady… he’s Tom Brady. He’s amazing.”
Williams showed no signs of the shoulder injury that ruled her out of the semi-finals of last week’s Yarra Valley Classic.
She has also been battling a lingering Achilles injury first sustained at last year’s US Open, but has been in strong form so far in Melbourne as she chases Margaret Court’s record Grand Slam tally.
Like Brady, Williams wound back the clock by thrashing her opponent in a one-sided contest.
“This was a good start, it was vintage Serena,” she said.
“Wasn’t sure how my serve would be after the shoulder (injury), but it’s feeling good.”
The 10th seed, competing in her 20th Australian Open, turned heads with her attire — a multi-coloured, one-legged catsuit inspired by late sprint queen Florence Griffith Joyner, popularly known as ‘Flo-Jo’.
She remains the fastest woman in history, holding the 100m best of 10.49sec set at the 1988 Seoul Olympics — a remarkable feat that was always under the shadow of suspicions that it was fuelled by drugs.
“I was inspired by Flo-Jo, who was a wonderful track athlete, amazing athlete when I was growing up,” Williams said.
“Watching her fashion, just always changing, her outfits were always amazing.
“The Nike team actually thought of this design of inspiration from Flo-Jo.
“I was like, ‘Oh, my God, this is so brilliant’.”
Williams, the seven-time Australian Open champion, will play Serbia’s Nina Stojanovic in the second round on Wednesday.