Medina Garrigues, of Spain, posted a 6-4, 4-6, 6-0 victory over Melanie Oudin of the United States, advancing to the second round.
The 20-year-old Oudin made it to the U.S. Open quarterfinals in 2009.
American McHale was bested by Canadian Aleksandra Wozniak 7-5, 5-7, 6-4. The Montreal native had to go 2 hours, 48 minutes, to beat her 19-year-old opponent.
Fourteenth-seeded Slovenian Polona Hercog, Argentine qualifier Paula Ormaechea and Stefanie Voegele of Switzerland also posted opening-round wins Monday.
2014: The Year in Music [PHOTOS]