The world number two and 17-time Grand Slam winner showed imperious form ahead of the French Open, beating world number 23 Cuevas to win the 85th title of his career in a thrilling second set tie break.
Federer showed dexterity and power despite resolute defence from his opponent, who required two injury timeouts for treatment on his wrist, to win through 6-3, 7-6 (13/11) in one hour 36 minutes.
"It's been a while since I won a title on clay," said a delighted Federer, whose last clay court title was Madrid in 2012. "It's been a pleasure playing here."
Federer has been given celebrity status in Istanbul over the last week on his first ever appearance in the country with banners around the court reading 'welcome to Turkey, king' and the crowd chanting his name.
In the first set, Federer raced to 4-1 lead in just 20 minutes, adapting better to the slow conditions on the red clay court after a heavy afternoon shower before the match.
He also showed none of the weakness on this first serve that had plagued his game earlier in the week.
Cuevas also showed fine touch in places both around the baseline and the net but was making too many unforced errors.
With Federer serving for the first set, Cuevas let out a howl of frustration as he missed the baseline yet again.
Cuevas' problems mounted in the second set when he called two injury timeouts for treatment from the trainer on his wrist.
Federer, on top of his game and thrilling the crowd, broke Cuevas in the seventh game with a well taken forehand volley.
But Cuevas shrugged off the injury and began to play potently from the baseline, seizing his chance to break back immediately and level to set at 4-4 and saved three break points on his own serve with some superb baseline play.
The second set went to a tie break with the pair beginning to exchange thrilling rallies.
Federer then took his mini-break when Cuevas badly mishit a forehand but Cuevas levelled with attacking play of his own.
Showing the tension, Cuavas double faulted but Federer missed a chance on match point when he pushed possible backhand winner into the tramlines.
Cuevas then himself missed an easy forehand volley on set point and Federer saved another set point with an outstanding backhand return winner.
But with Federer now playing some brilliant attacking tennis, he finally converted a match point to win the tie-break 13/11.
"I felt unlucky and then I felt lucky," was how Federer described the tie-break which was a fitting conclusion to Turkey's first ever ATP World Tour tournament.
"I think that the match deserved a third set," he added.