Azarenka advanced out of the second round with a 6-3, 7-6 (7-2) win over Czech qualifier Andrea Hlavackova, despite piling up nine double-faults.
The Belarusian -- last year's Madrid runner-up -- improved to 31-2 with the triumph. She'll next face 13th-seeded former world No. 1 Ana Ivanovic of Serbia, who downed Russian Nadia Petrova 7-5, 6-1 Tuesday.
Sharapova dispatched Klara Zakopalova of the Czech Republic 6-4, 6-3 on the clay courts of The Magic Box.
The Russian's win put her at 24-4 for the year. Her next opponent will be Czech Lucie Safarova, who topped Spanish wild card Carla Suarez Navarro 6-3, 6-4.
Ninth-seeded American Serena Williams decimated Russian Anastasia Pavlyuchenkova 6-2, 6-1 in an hourlong match, and will next face fellow former world No. 1 Caroline Wozniacki, who topped German Mona Barthel 6-4, 7-6 (7-2).
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