The American, who has only won two matches in four visits to Valencia, lost the opening set on a tiebreak after neither man could make an impact on the other’s serve.
And world number 21 Robredo got the all-important break in the penultimate game of the match before serving it out for a first win over Isner in four attempts.
Robredo will face Chinese Taipei’s Yen-Hsun Lu in round two.
Fourth seed Feliciano Lopez had an easier afternoon as he eased past Slovakian Norbert Gombos 6-4, 6-4 in little over an hour to set up a last 16 meeting with fellow Spaniard Pablo Carreno Busta.
France’s Gilles Simon was another seed to fall as he was swept aside by Alexandr Dolgopolov 6-0, 6-3.
The top three seeds David Ferrer, Thomas Berdych and Andy Murray all get their campaigns underway on Wednesday.-AFP