Sharapova will next play Dominika Cibulkova, who beat No. 16 Carla Suarez Navarro 6-1, 6-0 in 59 minutes. Suarez Navarro was clearly still fatigued from her 3-hour, second-round match in the extreme heat. She hit only two winners against Cibulkova.
"I finished the last match with pain. I tried to recover yesterday but it was not possible to play good today," she said after Saturday's defeat. "When you play with these players at this level, you need to be 90 percent perfect or 100 percent perfect. If you are less than this, you cannot play, you cannot be on court."
Stephens, 20, advanced to the fourth round with a 7-5, 6-4 win over Elina Svitolina of Ukraine.
Last year, Stephens made it to the fourth round or better at all four majors -- joining Serena Williams and Agnieszka Radwanska as the only players to achieve that feat. And Stephens, seeded 13th this year, beat Williams in last year's quarterfinals at Melbourne Park, one of only four losses for Williams in 2013.
Wozniacki now will have to wait until at least the French Open to claim an elusive first Grand Slam title. Muguruza Blanco won her first WTA tournament two weeks ago at the Hobart International.
The Associated Press contributed to this report.