The Briton double-faulted 10 times as she struggled with her serve but was still able to see off her American opponent 7-5 6-3 in Acapulco.
Watson, 24, plays second seed Kristina Mladenovic of France in round two.
Fellow Briton Kyle Edmund plays Sam Querrey of the US in the men's draw later on Tuesday.
Heather Watson moved into the second round of the Abierto Mexicano Telcel with a straight sets win over Bethanie Mattek-Sands.