The world number 60 won 6-2, 4-6, 7-5 against Merida, who was playing in his seventh match in the Romanian capital and his first tour final.
Navone missed two match points when serving for the title in the ninth game of the deciding set but later broke his opponent's serve to eventually get over the line.
It was seventh seed Navone's third ATP final after two previous defeats, including in Bucharest two years ago.