The former top-ranked Frenchwoman will play second-seeded Dinara Safina of Russia in the next round of the dual WTA and ATP tournament. Safina won her fourth title this season in Tokyo on Sept. 21 and is at a career-high No. 3 in the world rankings.
"I will be definitely the underdog for the next match," Mauresmo said.
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, has already pulled out because of an ankle injury.
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 before Cornet recovered to even the set at 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."