Temperatures moderated Saturday, ending a four-day heat wave in which players battled through temperatures well past 100 degrees Fahrenheit. The high Saturday was in the 70s.
Two-time defending champion and No. 2-seeded Azarenka won 11 straight games in a 6-1, 6-0 romp past Yvonne Meusburger in 60 minutes. Azarenka won two-thirds of the points on serve -- dropping the first service game of the day -- and an amazing 72 percent off Meusburger's serve.
Seven of the 12 points Meusburger managed to take when serving came defending break-point opportunities.
Sharapova, seeded third, defeated 25th-seeded Alize Cornet 6-1, 7-6 (8-6). Sharapova was coming off a 3-hour, 28-minute second-rounder but was still able to race through the first set Saturday in 32 minutes, taking 30 of the 43 points.
The second-set was closer, with Cornet having a set point in the tiebreaker before Sharapova put the win away.
Muguruza ousted 10th-seeded Caroline Wozniacki 4-6, 7-5, 6-3 in her first Grand Slam third-round match. Muguruza advanced through qualifying last week in Hobart in winning her first WTA title and hasn't slowed in Melbourne. She finished with seven breaks in the match, going 4-for-4 in break points in the third set.
The loss will cost Wozniacki her Top 10 ranking when the Australian Open ends.
Muguruza draws world No. 5-ranked Agnieszka Radwanska in the fourth round. Radwanska won about two-thirds of the points in the last two sets of a 5-7, 6-2, 6-2 win over 29th-seeded Anastasia Pavlyuchenkova.
Eighth-seeded Jelena Jankovic defeated Kurumi Nara 6-4, 7-5 with seven breaks while No. 11-ranked Simona Halep posted a quick 6-1, 6-4 rout of Zarina Diyas. Also Saturday, 13th-seeded Sloane Stephens beat Elina Svitolina 7-5, 6-4 and 20th-seeded Dominika Cibulkova claimed a slight upset in a big way, defeating No. 16 Carla Suarez Navarro 6-1, 6-0.
The wins by Azarenka and Stephens set up a rematch from last year's Australian Open semifinals, which Azarenka won 6-1, 6-4. Also in the fourth round in this section of the draw Muguruza, one of two unseeded women in the Round of 16, goes against Radwanska.
The other fourth-rounders have Sharapova drawing Cibulkova and Jankovic going against Halep.