Sharapova is the only former women's champion left after the exits of Venus Williams and Martina Hingis.
Sharapova beat Elena Dementieva 6-1, 6-4 in a match briefly interrupted by a male streaker in the second set. Mauresmo beat Anastasia Myskina 6-1, 3-6, 6-3.
Mauresmo has a 2-0 edge against Sharapova, both straight-sets wins on hard courts.
Mauresmo, who turned 27 yesterday, lost in the semi-finals at her three previous Wimbledons.
"I don't think I have anything to prove to myself, first of all, or to anybody. I just want more," Mauresmo said.
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