Goerges, 22, dispatched her opponent 6-1, 6-2 in 63 minutes at The Fairmont Acapulco Princess.
Joining her with Day 1 wins were No. 6 seed Arantxa Parra Santonja of Spain, who bested Austria's Sybille Bammer 7-6 (7-3), 7-6 (7-4), and France's Pauline Parmentier, who downed Czech Zuzana Ondraskova, 6-3, 7-5.
Romania's Sorana Cirstea also notched a victory, defeating Austrian Patricia Mayr-Achleitner, 6-2, 6-4.
Last year's champion, Venus Williams, is not returning to defend her crown, while the 2010 runner-up, Slovenia's Polona Hercog, is seeded second this year.
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