Cornet, an 18-year-old Frenchwoman, broke to take a 3-2 lead in the second set, but the former top-ranked Mauresmo won the next four games to even the match at one set apiece.
In the third, Mauresmo led 2-0 and but Cornet recovered to 3-3. Mauresmo later won nine consecutive points and served out the match.
"It's always difficult and not very comfortable to play another Frenchwoman,'' Mauresmo said. "Yes, it was tight, but we showed some good things, sometimes a little bit up and down, but overall (it was) a pretty good match.''
Mauresmo will face second-seeded Dinara Safina of Russia in the next round of the dual WTA and ATP tournament.
"I will be definitely the underdog for the next match,'' Mauresmo said.
Safina won her fourth title this season in Tokyo on Sept. 21 and is at a career-high No. 3 in the world rankings.
The women's field at the Kremlin Cup contains seven of the top 10 players in the world, including top-ranked Jelena Jankovic of Serbia.
U.S. Open champion Serena Williams, last year's runner-up in Moscow, pulled out because of ankle injury, however.
In the men's event, Jeremy Chardy of France rallied to beat Potito Starace of Italy 3-6, 6-1, 6-4, and Guillermo Garcia-Lopez of Spain advanced by beating Nicolas Devilder of France 6-2, 6-4.
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