Henin, a former world No. 1 who has returned to the game after a brief retirement, needed 64 minutes to eliminate Craybas 6-2, 6-2. That set up a second-round match with fifth-seeded Elena Dementieva.
Mariya Koryttseva got past Kristina Barrois 2-6, 6-3, 6-3, a victory that gives her a matchup with seventh-seeded Jelena Jankovic.
Jankovic is coming off her victory last week at the BNP Paribas Open in California.
The woman Jankovic defeated for that championship, Carolina Wozniacki, will play Tsvetana Pironkova in the second round. Pironkova advanced Wednesday with a 6-4, 6-2 decision over Heather Watson.
Other first-round winners Wednesday included Patty Schnyder, Kimiko Date Krumm, Ekaterina Makarova, Carla Suarez Navarro, Sofia Arvidsson, Andrea Petkovic, Sara Errani and Roberta Vinci.
The 32 seeded players received a bye past the opening round. Defending French Open champion Svetlana Kuznetsova is the No. 1 seed, followed by Wozniacki, Venus Williams, Victoria Azarenka and Dementieva.