Robredo claimed a 6-4 6-4 success in one hour and 25 minutes.
Argentinian wild card Guido Pella produced a notable upset by beating Spain's Guillermo Garcia-Lopez in straight sets.
The first set went to a tie-break after one service break apiece, but world number 108 Pella took it and the left-hander went on to complete a 7-6 (8/6) 6-4 win over a player ranked 56 places above him.
Fifth seed Marcel Granollers of Spain came through a three-set battle lasting just 10 minutes short of three hours as he saw off Slovenia's Aljaz Bedene 7-5 3-6 6-2.
Argentina's Carlos Berlocq swept aside Joao Sousa 6-4 6-2, but compatriot Federico Delbonis went out, going down 3-6 7-5 6-1 to Spain's Pablo Andujar.