Robredo had lost his previous three meetings with Isner and saw a match point go begging when the two met in the China Open earlier this month.
However, the Spanish world number 21 - one of the highest-ranked players in the field not to be seeded - emerged victorious on this occasion, triumphing 7-6 (7-3) 6-3 in an hour and 21 minutes.
Isner is renowned for his big serve, yet it was his opponent who proved unbreakable, winning 43 out of 47 first-service points and saving each of the five break points he faced.
Robredo will now face Lu Yen-Hsun in the second round of the ATP 500 hard-court event and needs three more wins to reach 500 in his career.
There was another high-profile exit on Tuesday as eighth seed Gilles Simon was routed 6-0 6-3 by Alexandr Dolgopolov.
However, fourth seed Feliciano Lopez claimed his first win at the tournament for five years, beating qualifier Norbert Gombos 6-4 6-4, while Kevin Anderson - the seventh seed - progressed with a 6-3 6-4 success against Philipp Kohlschreiber.
Fabio Fognini, Jeremy Chardy and Dusan Lajovic were also winners in straight sets, seeing off respective competition from Albert Ramos-Vinolas, Malek Jaziri and Joao Sousa.
The 2004 Valencia Open champion, Fernando Verdasco, had to work harder for a 6-4 3-6 6-3 win against Argentina's Leonardo Mayer.
Verdasco will face David Ferrer in round two, providing the top seed can make it past Andreas Seppi on Wednesday.