Garrigues dropped the first set to Lourdes Dominguez Lino but lost just three games the rest of the way for a 4-6, 6-2, 6-1 win.
Third-seeded Tathiana Garbin also lost her first set 4-6 before steadying and claiming a 4-6, 6-3, 6-3 decision over Catalina Castano.
Two other seeded players -- No. 5 Timea Bacsinszky and No. 6 Alisa Kleybanova -- had much easier times Tuesday. Bacsinszky defeated Nadia Lalami 6-2, 6-4 while Kleybanova was a 6-2, 6-3 winner over Aleksandra Wozniak, who was the runner-up at the Moroccan Grand Prix in 2007.
Also Tuesday, Greta Arn beat Jelena Dokic 6-4, 6-2 and Rossana De Los Rios topped Lilia Osterloh 6-4, 6-4. Other first-round winners were: Petra Cetkovska, Arina Rodionova, Anastasia Pavlyuchenkova and Emilie Loit.
2014: The Year in Music [PHOTOS]