The five-time Australian Open champion later withdrew from the doubles, avoiding any extra exposure to the blazing sun during the once-in-a-century heat wave that was gripping Melbourne for a fourth straight day.
Two-time finalist Li Na, the major threat to top-ranked Williams in the top half of the women's draw, had to save a match point before coming back to beat No. 26-seeded Lucie Safarova 1-6, 7-6 (2), 6-3 in 2 hours, 37 minutes.
Li, the 2011 French Open champion, later joked that she needed the match practice "because I think the weather is not warm enough."
Williams didn't face any serious danger in her win over No. 31-seeded Hantuchova, whose only win in 10 head-to-head matches came in the corresponding round at the 2006 Australian Open.
Williams was off the court in 1 hour, 20 minutes, and has conceded just 12 games in three straight-set wins this week.
She equaled Margaret Court's Australian Open mark of 60 match wins with her second-round victory, and beat that in the third round when she also matched Lindsay Davenport's record of 69 main-draw matches here in the Open era. That means she'll set another record just by showing up on Sunday against former No. 1-ranked Ana Ivanovic, who beat 2011 U.S. Open champion Sam Stosur 6-7 (8), 6-4, 6-2 in a night match.
"It was a tough match ... it's definitely hot, but you have to be ready to play," she said. "And then you have to prepare yourself mentally, too."
The temperature hit 39 Celsius (102 Fahrenheit) during Williams' match and topped 42 C (108 F) by the mid-afternoon, but humidity remained low and there was no reason for organizers to invoke the Extreme Heat Policy and suspend matches for the second day in a row. The temperatures dipped to 32 C (90 F) before the night matches as a cool change kicked in, and dropped by another 10 degrees before play ended Friday.
Williams has won 24 matches dating back to August, carrying momentum from her dominating 2013 into a new season. She won 78 of her 82 matches and won 11 titles last year, and seems to be getting better with age.
"I feel like, in life 32 is young. In sports it's old," she said. "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."
The Williams sisters were entered in the doubles but withdrew after Serena's singles match Friday, citing a leg left injury for Venus.
"I love playing doubles, love playing with Venus, but sometimes it doesn't work out," she said.
Rod Laver Arena was about three-quarters full for the match, though it was a quiet crowd — people seemed to be expending more energy fanning themselves with programs and newspapers than applauding points on the court.
No. 9 Angelique Kerber advanced earlier with a 6-3, 6-4 win over American Alison Riske, and said her main aim had been to "get off the court before it became really hot." Kerber will next play No. 28 Flavia Pennetta, who advanced 6-1, 7-5 over Mona Barthel of Germany.
No. 22 Ekaterina Makarova advanced with a 6-4, 6-4 win over Monica Niculescu and No. 30 Eugenie Bouchard beat American Lauren Davis 6-2, 6-2 to set up a fourth-round match against Australian wildcard entry Casey Dellacqua, who beat 2010 semifinalist Zheng Jie of China 6-2, 6-4.
On the men's side, third-seeded David Ferrer advanced to the fourth round for a 10th consecutive Grand Slam when he beat No. 29 Jeremy Chardy 6-2, 7-6 (5), 6-2. The French Open finalists will next play Florian Mayer, who beat No. 20 Jerzy Janowicz 7-5, 6-2, 6-2.
No. 7 Tomas Berdych beat Bosnian qualifier Damir Dzumhur 6-4, 6-2, 6-2 and will next play No. 19 Kevin Anderson, who beat Edouard Roger-Vasselin 3-6, 4-6, 6-3, 7-6 (5), 7-5.