Cuevas, who triumphed at the Swedish Open only a fortnight ago, ran out a 6-3 6-4 winner in the final of the ATP 250 clay-court event.
The world number 60, who gained his place in the event as a qualifier, saw his dream month continue on Sunday as he first beat top seed Fabio Fognini to reach the final.
After the semi-finals were delayed by rain on Saturday, Cuevas and Robredo each progressed in straight sets, the latter defeating Marin Cilic.
And Cuevas showed no sign of fatigue as he subsequently maintained his 100 per cent record in ATP finals.
Cuevas claimed a crucial break when 3-2 ahead in the first set, after Robredo had staved off three earlier break points.
The Uruguayan held serve thereafter to seal the set before making an ideal start to the second.
After breaking Robredo in the opening game, Cuevas stretched his lead to 4-1 before his opponent hit back with a break of his own.
Robredo's late rally, in his 20th World Tour final, proved in vain as Cuevas held to love when serving for the match.