The two Italians each moved on with straight-set wins over Spanish opponents on the red clay at the Fairmont Acapulco Princess.
Vinci defeated Silvia Soler-Espinosa 6-2, 7-6 (7-5), while Pennetta -- who won the Mexican Open in 2005 and 2008 and was runner-up four other times -- had little trouble in her 6-4, 6-2 triumph over Arantxa Parra Santonja.
Third-seeded Sara Errani of Italy also breezed into the second round with a 6-1, 6-1 rout of American Irina Falconi.
But the news wasn't as good for another seeded player as No. 5 Alexandra Dulgheru of Romania was upset by Slovakian Magdalena Rybarikova, 2-6, 7-5, 7-6 (7-3).
2014: The Year in Music [PHOTOS]