Souza broke Haase late in each set, serving to close out the match for his first win of the year. Haase, ranked 45th, had four chances to break the Brazilian's serve, but couldn't capitalize on them.
Seventh-seeded Leonardo Mayer was also eliminated, losing to fellow-Argentine Guido Pella 6-7 (4), 7-6 (3), 6-7 (4) in 2 hours, 37 minutes at the event won by Rafael Nadal last year.
Mayer, served 11 aces and had five break opportunities in the final set while Pella had one, but each player broke each other only once.
Tommy Hass of Germany is the tournament's top seed.