The second-seeded Robredo had two break points at 1-1 in the first set, but it was Cuevas who first broke in the sixth game for a 4-2 lead.
Cuevas took an early 2-0 lead in the second set and broke the 32-year-old Robredo's serve once more in the fifth game. Robredo had a break point to level to 4-4.
Robredo hit 36 winners compared to Cuevas' 26, but had 36 unforced errors against 19 for Cuevas.
Cuevas won his maiden ATP title earlier this month at the Swedish Open in Bastad. He is the second qualifier to win an ATP World Tour tournament this year after Slovakia's Martin Klizan at Munich in May.