Mauresmo led 4-1 in the tiebreaker at Ariake Colloseum, but Cibulkova fought back and took a 9-8 lead with a crosscourt forehand before winning when Mauresmo's return went long.
"The match was really close in the third set,'' Cibulkova said. "I thought I should have closed it out earlier ... but I fought through and was able to win the match.''
Mauresmo blew four match points, including one in the tiebreaker.
"It's always frustrating to lose a match when you have match points and can't close it out,'' Mauresmo said. "I let her get back into the match in the second set and it's disappointing to lose like that.''
In other first-round matches, Italy's Francesca Schiavone upset seventh-seeded Daniela Hantuchova of Slovakia 6-1, 7-5 while Kaia Kanepi of Estonia defeated eighth-seeded Anna Chakvetadze of Russia 6-4, 3-6, 6-3.
Marion Bartoli of France cruised to a 6-2, 6-2 win over Russia's Maria Kirilenko, Flavia Pennetta of Italy downed Israel's Shahar Peer 6-4, 6-4 and Japan's Ayumi Morita defeated Agnes Szavay of Hungary 6-7 (7), 7-5, 6-4.
Alize Cornet of France rallied to defeat qualifier Aleksandra Wozniak of Canada 4-6, 6-3, 6-3.
No. 1 seed Jelena Jankovic has a bye into the second round, along with fellow Serb Ana Ivanovic, who is second-seeded.
In women's doubles, Vania King of the United States and Nadia Petrova of Russia defeated the top-seeded pair of Ai Sugiyama of Japan and Slovenia's Katarina Srebotnik 6-4, 6-4.
Sporting Injury Worries Lessen
Pablo Remaining Positive
