Robredo, who titled in Buenos Aires in 2009, dispatched fellow Spaniard Pablo Carreno Busta 6-4, 6-4 to move on the second round, where he will face Argentine wild-card Guido Pella.
Pella advanced with a 7-6 (8-6), 6-4 victory over Guillermo Garcia-Lopez.
Also among the Day 1 winners was No. 5 seed Marcel Granollers of Spain, who outlasted Slovenia's Aljaz Bedene 7-5, 3-6, 6-2 in a 2-hour, 49-minute marathon.
His next opponent will be Spain's Pablo Andujar, who dropped the first set against Argentine Federico Delbonis but bounced back for a 3-6, 7-5, 6-1 triumph.
Unseeded Carlos Berlocq of Argentina also made the second round with a 6-4, 6-2 win over Portugal's Joao Sousa.
Swim Week Miami Beach 2014 [PHOTOS]