And ninth seed Daniela Hantuchova saw off France's Alize Cornet 6-2 7-5 to continue her progress.
Former world No. 1 Azarenka beat France's Alize Cornet 4-6 6-3 6-1 despite dropping serve six times.
Like Sharapova, Australian Open champ Victoria Azarenka struggled with her serve, but she rallied past Frenchwoman Alize Cornet 4-6, 6-3, 6-1.
In Austria, Belgian second seed Yanina Wickmayer will play France's No. 2 Alize Cornet in Sunday's final of the Bad Gastein tournament.
Another Frenchwoman, Alize Cornet, stands between her and a place in the semifinals and a 13th straight win on the hard courts of the Farum Arena.
The 2000 doubles winner's third round opponent is French 15th seed Alize Cornet, who subdued a vociferous home crowd in outclassing China's Peng Shuai 6-2 6-2.
Alize Cornet ended the hopes of 19-year-old American Lauren Davis, who was allowed into the main draw when second seed Victoria Azarenka pulled out due to ongoing ankle problems.
In second round action Tuesday, Serena Williams needed exactly one hour to reach the quarterfinals with a crushing 6-2 6-2 win over France's Alize Cornet in the night session.
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Williams beat Alize Cornet 6-3, 6-3 in the match preceding the Djokovic-Harrison encounter at Rod Laver Arena, which will be the likely venue for her big matchup Friday against Sharapova.
Bethanie Mattek-Sands defeated Alize Cornet 7-6 (9-7) 7-5 for her first singles win in the women's teams tournament, while Melanie Oudin beat debutant Pauline Parmentier 6-4 6-4 in the second rubber.
Seeds Agnieszka Radwanska, Flavia Pennetta, Alisa Kleybanova, Agnes Szavay, Sybille Bammer and Aleksandra Wozniak also advanced, but Alize Cornet, Dominika Cibulkova, Zheng Jie, Ai Sugiyama and Sara Errani failed to progress.
Williams, whose last grand slam title came at Wimbledon in 2008, booked her place in the third round with a comfortable 6-3 6-3 win over Alize Cornet on Rod Laver Arena.
Baltacha will face Anastasia Rodionova in the next round after the Australian beat Alize Cornet 2-6 6-3 7-5, and the Briton will be looking for revenge after losing to her in the final round of US Open qualifying last year.
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