Kleybanova, the tournament's No. 3 seed, fought off five break points in a 6-1, 6-1 win over Lu Jing-Jing. Kleybanova won 65 percent of the points on serve and took more points (35-28) when receiving than Lu managed to win on serve.
Kleybanova was one of four players to lose no more than two games Tuesday in moving to the second round.
Second-seeded Marion Bartoli rolled through a 6-0, 6-1 victory over Maria Elena Camerin. Bartoli cashed in seven of nine break-point chances and Camerin avoided a shutout by breaking Bartoli's serve in the match's next-to-last game.
No. 8-seeded Bojana Jovanovski needed a mere 42 minutes to rout Tamarine Tanasugarn 6-0, 6-1. Jovanovski won 73 percent of the points in the match. Also, Dinara Safina capped Tuesday's play with a 6-2, 6-0 win over Han Xinyun in 53 minutes. Safina had seven breaks in seven Han service games.
Fourth-seeded Jarmila Groth also advanced, defeating Sun Shengnan 7-6 (7-2), 6-3, but No. 7-seeded Kimiko Date-Krumm dropped a 4-6, 6-2, 7-6 (7-5) decision to Anne Kremer.
Other first-round matches saw Kurumi Nara top Elena Bovina 6-3, 6-3; Michaella Krajicek oust Tatjana Malek 6-3, 6-2; Misaki Doi win 6-2, 6-3 over Tetiana Luzhanska; and Ekaterina Ivanova beat Nina Bratchikova 6-3, 4-6, 6-4.