Sharapova, who won last week's event in San Diego, managed to win in a tiebreak (7-5) in the first set and had a 3-1 edge in the second when Daniilidou said she could not continue.
Also winning was No. 2 seed Jelena Jankovic, who was a 6-1, 6-1 victor over Shuai Peng. Third-seeded Ana Ivanovic defeated Ashley Harkleroad 6-4, 6-2, while Nadia Petrova, the fourth seed, was a 7-5, 6-3 survivor against Lilia Osterloh.
Elena Dementieva, the defending champion, defeated Madison Brengle 6-2, 6-0.