The 2006 U.S. Open semifinalist faced just three break points, but Robredo converted his only one in the third to win the set.
Robredo was the lowest-ranked man left in draw at No. 41. He won his matches in the second and third rounds when his opponents retired.
Robredo has advanced to the fourth round in seven of his 10 trips to the U.S. Open — and has lost that match every time. He was one of a record six Spanish men to reach the fourth round.