Both competitors were evenly matched in the early stages, which resulted in the first set being decided by a tie-break.
It was a battling exchange between the pair as Isner edged the contest 15-13 to take the lead in Paris.
The intensity continued on the clay court in the second set as another tie-break was required, which, once again, Isner won more comfortably 7-3.
After a brief delay due to rain, both players stayed on serve for the remainder of the third set, resulting in yet another tie-break.
Robredo was victorious this time, sending the match into a fourth set, but just one break from Isner was needed for the American to secure a place in the next round.