Williams, aiming for a third consecutive major title, recovered from a break down in the second set to win six straight games and finish off a 6-1, 6-3 win over Japan's Ayumi Morita in 66 minutes.
The 15-time major winner even surprised herself with another serve at 128 mph (207 kph), matching her career fastest serve she hit earlier in the tournament.
"I tried to hit it really hard. I hit 207 (kph) the other day and I thought it was luck," she said. "But I did it again and I was like whew! I'm going to try to go for 210. We'll see."
Top-ranked Azarenka struggled to hold off injured American Jamie Hampton 6-4, 4-6, 6-2, and didn't help herself with six double-faults.
Hampton, who needed a medical timeout for a lower back problem before she served out the second set and winced in pain, frequently on the verge of tears, throughout the third, still managed to hit 41 winners to keep the Belarusian under pressure.
Azarenka appeared frustrated at times, but overcame an early break and fended off triple break point in the seventh game of the deciding set before clinching the match in 2 hours, 9 minutes.
"She played incredible, went for every single shot. I felt it was touching every single line," Azarenka said. "She took a medical timeout but she rips winners all over the place and I was like, 'Can I have a back problem?' I'm feeling great, but I'm missing every shot."
After wasting two set points on Azarenka's serve late in the second set, Hampton had to leave the court for nine minutes to have treatment on her back.
Azarenka practiced her backhands and serve while Hampton was in the locker room, but the break didn't help her immediately. Hampton returned and held in the next game and needed more treatment in the break at the end of the set.
Even with the pain of two herniated disks, the 23-year-old Hampton, from Auburn, Ala., went down swinging — making 47 unforced errors to go with the winners that caught Azarenka off guard and had her asking, loudly at one point, what she could do to counter them.
Sensing an upset, and stirred by the obvious signs of pain, the crowd on Rod Laver Arena got right behind the No. 63-ranked Hampton, who had never previously gone past the second round at a major.
Azarenka had her share of supporters in the stands, too, including friend and musician RedFoo who was wearing a shirt emblazoned with "We Go Hard" across the front.
If results go according to rankings, Azarenka and Williams will meet in the semifinals. Williams has won the Australian Open five times and is on a 19-match winning streak — and she has lost only one match since her first-round exit at the French Open last year.
Considering Azarenka has lost 11 of their 12 meetings, including all five in 2012, it's a potential matchup where Azarenka will have to play better than ever.
But they both have to advance to the last four, something Williams failed to do here last year when she was knocked out in the fourth round.
In the corresponding round this year, the 31-year-old American will meet No. 14 Maria Kirilenko, who beat No. 20-Yanina Wickmayer 7-6 (4), 6-3. Azarenka next plays Elena Vesnina, who beat 16th-seeded Roberta Vinci of Italy 7-6 (4), 6-4.
Elsewhere, two-time major winner Svetlana Kuznetsova advanced with a 6-2, 4-6, 6-3 win over Spain's Carla Suarez Navarro.
On Friday night, Maria Sharapova celebrated with extra exuberance after her 6-1, 6-3 win over Venus Williams, her first victory over the seven-time major winner in a Grand Slam.
"I was just really pumped," she said. "Why shouldn't I be?"
After back-to-back 6-0, 6-0 wins in the first two rounds — the first time that happened at major since 1985 — Sharapova has conceded the fewest number of games en route to the fourth round at the Australian Open since Steffi Graf did so 24 years ago.
Graf also lost only four games in her first three matches on her way to the second of her three consecutive titles in Melbourne.
Top-ranked Novak Djokovic took another step closer to a third consecutive Australian title, defeating Radek Stepanek 6-4, 6-3, 7-5 in the third round.
His victory came on the same day Lance Armstrong admitted during a television interview with Oprah Winfrey that he used banned drugs to win his seven Tour de France titles. Djokovic, a lifetime cycling fan, said at his post-match news conference that it was "a disgrace for the sport to have an athlete like this."
"He cheated the sport," Djokovic said. "He cheated many people around the world with his career, with his life story."
Djokovic will play Sunday against No. 15 Stanislas Wawrinka, who knocked out the last American man in the draw with a 7-6 (6), 7-5, 6-4 win over No. 20 Sam Querrey.
Fourth-seeded David Ferrer finished off a 6-4, 6-2, 6-3 win over 2006 Australian finalist Marcos Baghdatis with an ace, advancing to a fourth-round match against Japan's Kei Nishikori.
No. 5 Tomas Berdych beat Austria's Jurgen Melzer 6-3, 6-2, 6-2 and will next play South Africa's Kevin Anderson. Djokovic's Serbian Davis Cup teammate Janko Tipsarevic advanced to a meeting with No. 10 Nicolas Almagro.
In an all-Serbian match of two former No. 1 women, 2008 French Open champion Ana Ivanovic beat Jelena Jankovic 7-5, 6-3.
She moved into the fourth round against Poland's Angieszka Radwanska, who is seeded No. 4 and won her 12th straight match — including titles at Auckland and Sydney — with a 6-3, 6-1 defeat of Britain's Heather Watson.
No. 5 Angelique Kerber and No. 19 Ekaterina Makarova, two of the four women who beat Serena Williams in 2012, will meet in the fourth round.
Kerber stopped 17-year-old American Madison Keys 6-2, 7-5 to celebrate her 25th birthday. Makarova had a 6-7 (4), 6-3, 6-4 win over 2007 Wimbledon finalist Marion Bartoli.