In ominous form after winning the Brisbane International warm-up event, the American did not concede a point on her first serve under the lights of Rod Laver Arena and roared to her 23rd straight victory.
A former girls' champion at Wimbledon, 155th-ranked Barty has been touted as the future of tennis in Australia.
After ending a sequence of losing games, the 17-year-old raised her arms aloft in mock triumph when she held serve in the fifth game of the second set, sparking a rare roar from the crowd.
"I just think she's so cute," Williams told reporters. "I like her a lot. She's so young.
"I'd like to see her do really well. I think she has a game to do really well," added the world number one after setting up a clash with Serbia's Vesna Dolonc.
A five-times champion at Melbourne Park, Williams has not won the event since 2010 and was hampered by foot injuries in 2012 and 2013.
The 32-year-old appears in peak fitness this year and made a conscious effort to race to the net whenever an opportunity arose.
"It's just something I think I need to do," said Williams. "I've been doing it for a while. I just haven't been actually coming in.
"In my mind I've been at the net but now I'm physically going there a little more. No pressure. My next match I might stay at the baseline the whole time.
"It's nothing I'm permanently working on. I'm just trying to have fun and do what I want to do out there."
Williams, who can match the Grand Slam tally of Chris Evert and Martina Navratilova with triumph at Melbourne Park, could face world number 104 Dolonc in stifling heat on Wednesday with temperatures forecast to exceed 40 degrees Celsius (104 Fahrenheit) in the coming days.
"It's okay. I have to be ready for it," she said. "I'm happy to be in the second round so I can't complain about the weather at this point.
"It doesn't matter whether I win or lose as long as I have fun. As long as I'm able to stay relaxed, I'll be okay."
- Sports & Recreation