Halep, the third-seeded Romanian, lost to France's Mathilde Johansson 7-6 (7-5), 7-5 during a rainy day on the red clay courts of Club Campestre El Rancho.
No. 8 seed Garrigues was ousted by longtime Colombian crowd favorite Catalina Castano, who prevailed in a 7-6 (7-5), 2-6, 7-6 (7-5) epic that took 3 1/2 hours to complete.
Also scoring wins on opening day were Austrians Patricia Mayr-Achleitner and Yvonne Meusburger.
A scheduled match between No. 1 seed Julia Goerges and Olivia Sanchez was postponed until Tuesday due to rain.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need