Azarenka, the No. 14 seed, dispatched No. 127-ranked qualifier Naomi Osaka 6-1, 6-1 in a scant 56 minutes. But Muguruza was stunned earlier in the day by Barbora Strycova 6-3, 6-2, joining No. 2 seed Simona Halep as an upset victim.
Azarenka, seen by oddsmakers as the second-best bet to win this tournament behind No. 1-seeded Serena Williams, has beaten Strycova in all four of the matches they've played, winning all eight sets.
It was the first time in the Open era at the Australian Open that two of the top three women's seeds were eliminated before the fourth round. And yet, it was the fifth time in the past eight majors that two of the top three women's seeds failed to reach the round of 16. The last time that happened on the men's side was the 2004 French Open.
Azarenka has dropped only five games in three matches. Osaka, 18, was one of four teenagers to advance to the third round. She was born in Osaka, Japan, but moved to the United States as a 3-year-old and claims dual citizenship. This was her Grand Slam main draw debut.
Azarenka, a 26-year-old Belarusian, has now lost only 22 games in her 8-0 run to begin 2016 and is hopeful to advance deep in the draw based on her recent performance.
"I just try to focus on my execution more," Azarenka said. "I mean, the score doesn't really tell -- say pretty much the whole story sometimes. But I'm pretty happy with the way I'm playing. I just, you know, I want to still keep improving from match to match, because it's only getting harder from here."
She admitted to being caught off guard in the early going against Osaka.
"She definitely surprised me with her play," Azarenka said. "I think in the first game you could see that I was a little bit off my timing because I was expecting some bombs coming my way and the ball came pretty slow."
"I think she has an interesting game. I think she has a lot of potential, has a lot of power. I'm sure we will see a lot more of her."
At the end of her surprising rally to the third round, Osaka was upbeat and ambitious about her goals.
"To be the No. 1 and to win a lot of Grand Slams and to play Fed Cup and then to play the Olympics and to be happy," Osaka said.
Strycova, 29, is ranked No. 48 among WTA players and was only 2-18 versus top-five players coming in, but one of those matches came at Wimbledon in 2014, when she surprised Li Na in the third round. A native of the Czech Republic, Strycova has now won all six sets in Melbourne and has produced her finest effort at the Australian Open.
Muguruza, 22, was a finalist last year at Wimbledon, one of only five players born in the 1990s to reach a Grand Slam final.
Afterward, Muguruza lasted for only three questions in her postmatch news conference.
"Clearly not my best, for sure," said Muguruza, a Venezuelan-born Spaniard. "I think today is a very bad day, you know, at the office. I think Barbora played good, very good. Also, I didn't play good.
"But, I don't know, I think I just couldn't find the court, my shots. Yeah. Didn't really find my game."
Strycova doesn't seem concerned about her winless record against Azarenka.
"Well, I lost also against Garbine in Tokyo pretty easy, and I won today," Strycova said. "So I will go to that match with confidence. I have to play my best tennis and to mix it and try to somehow win and focus on every point.
"But Victoria is very, very good. I saw her hitting some balls yesterday, and she's hitting the ball very well. But we don't know how it goes."
Angelique Kerber has advanced to the fourth round after beating Madison Brengle 6-1, 6-3. No. 7-seeded Kerber's win on Saturday makes her the highest-ranked player in the bottom half of the draw, following Muguruza's loss.
Kerber, a two-time Grand Slam semifinalist, faces compatriot Annika Beck of Germany in the fourth round.
Sydney-born Johanna Konta, who beat Venus Williams last Tuesday, became the first British woman to reach the fourth round at the Australian Open since 1987 when she beat Denisa Allertova 6-2, 6-2. Her next match is against 2015 semifinalist Ekaterina Makarova, who had a 6-3, 6-2 win over No. 9 Karolina Pliskova.
The Associated Press contributed to this report.