The Spaniard - a two-time semi-finalist in Cincinnati - downed his Serbian counterpart 7-6 7-5 in one hour and 47 minutes to move into the last eight of the tournament.
The defeat marks a second premature elimination for Djokovic in the space of a week, having suffered a third-round loss to Jo-Wilfried Tsonga in the Rogers Cup last Thursday.
Nothing could separate the pair tonight as the duo went blow for blow, but Djokovic was one game away from a one-set lead after leading 6-5 in games.
However, Robredo held serve to force a tie-break and went on to beat the top seed 8-6 en route to an early advantage in the best-of-two encounter.
The second set went the same way as neither player could establish any breathing space but, with Robredo leading 6-5, the world number 16 produced a timely break of serve to book his place in the quarters.