The 12th-seeded Cibulkova improved to 4-1 in head-to-head matches against the unseeded Garrigues after dispatching her in in 1 hour, 36 minutes at Ariake Coliseum.
Cibulkova will next face the winner of Monday's first-round match between Vania King of the United States and China's Zheng Jie.
In other first round matches, 14th-seeded Roberta Vinci of Italy beat Barbora Zahlavova Strycova of the Czech Republic 6-4, 4-6, 7-5 while Serbia's Jelena Jankovic overpowered Belgium's Yanina Wickmayer 6-3, 6-3.
Japanese wild card Ayumi Morita defeated Sorena Cirstea of Romania 6-2, 3-6, 6-2 while Croatia's Petra Martic recovered from a poor start for an 0-6, 6-4, 6-3 win over Germany's Andrea Petkovic.
Top-ranked Victoria Azarenka has a first-round bye as does second-seeded Maria Sharapova, who won here in 2005 and 2009. The $1.2 million tournament features 12 of the top 13 players in the world rankings.