Sousa sped past the Austria's Melzer 6-4, 6-3 on the clay courts at the Fairmont Acapulco Princess.
Spain's Pablo Andujar, however, fared better, moving on to the second round with a 3-6, 7-5, 6-2 victory over Serbian Dusan Lajovic.
Other Day 1 Acapulco winners Monday included Martin Alund of Argentina, Colombian Santiago Giraldo and Leonardo Mayer of Argentina.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'