No. 1 seed Vinci bested American Coco Vandeweghe in straight sets, 7-5, 7-5, at Sierra Madre Tennis Club.
Second-seeded Errani breezed past Stephanie Dubois of Canada 6-2, 6-2.
Romanian Alexandra Cadantu and Nina Bratchikova of Russia also posted Monday victories at Monterrey.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut