In the men's draw, second-seeded Igor Andreev advanced when Taiwan's Yen-hsun Lu retired with a right ankle injury after losing the first set 6-2.
Mauresmo, a finalist in 2003 long before 18-year-old Cornet turned pro, rallied from a break down in the second set, winning four games in a row to even their match at one set apiece.
In the third, Mauresmo led 2-0 and but Cornet recovered to 3-3. Mauresmo won nine consecutive points and served out her third consecutive win over Cornet, who has reached three finals this year and won one. Mauresmo has yet to reach a final this year.
"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.
Dominika Cibulkova of Slovakia progressed when Marion Bartoli of France retired with a left toe injury while trailing 6-1, 4-1, and Russian wild card Vera Dushevina upset Nicole Vaidisova of the Czech Republic 6-1, 3-6, 6-3 to set up a match with new No. 1 Jelena Jankovic.
The women's field at the Kremlin Cup contains seven of the top 10 players in the world.
U.S. Open champion Serena Williams, last year's runner-up in Moscow, pulled out because of an 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, Guillermo Garcia-Lopez of Spain advanced by beating Nicolas Devilder of France 6-2, 6-4, and Fabrice Santoro of France overcame Yuri Schukin of Kazakhstan 4-6, 7-6 (2), 6-4.
Mauresmo advances at Kremlin Cup
Maniche Suffers Back Injury
