The world number one had lost their only other encounter at Melbourne Park, in the third round in 2006 when the Slovak beat her in straight sets, but she made no mistake this time around.
Williams looked as if she was conserving energy and doing just enough to get through the match as the temperature touched 38 Celsius (100 Fahrenheit), and relied on her booming serve and blistering forehand to get her out of trouble on crucial points against the 31st seed.
The American, seeking her sixth Australian Open title, will now meet 14th-seeded Serbian Ana Ivanovic in the fourth round.
The win was a record 61st for Williams at the Australian Open, putting the American past Australian Margaret Court's 60.
Williams defeated Romania's Irina Spirlea, a former top 10 player, in her Melbourne Park debut in 1998 before being beaten in the second round by Venus.
"Felt good," Williams, who practised on public courts in Compton, a tough inner-city suburb of Los Angeles, said of her first trip Down Under.
"I definitely wanted to be here, and I don't remember my first impressions. As a kid, you don't particularly dream of - especially where I'm from. I never thought I would be in Australia.
"For me, it was a great opportunity to see a land that's so far away that you don't go to even in your dreams."
Williams has won five titles at Melbourne Park since her debut at the year's first grand slam 16 years ago and is a hot favourite to win a sixth after a dominant season last year when she won the French and US Opens.
"I feel like, in life, 32 is young. In sports, it's old," she added.
"But for whatever reason, I feel like I just never was really able to reach my full potential, and I feel like recently I just have been able to do a little better.
"I just keep trying to improve on everything."
Williams has teamed up with Venus for four doubles titles at Melbourne Park, but the celebrated sisters cancelled their bid for a fifth on Friday, with Venus withdrawing due to a leg injury.