The Dane got off to a strong start, but he ran out of steam in the third set. The final scoreline was 6-3, 3-6, 2-6.
Moller, ranked 181 in the world, entered the final as the underdog against Croatia's Dodig, who sits a few spots above the Dane in the world rankings at number 174.
In the deciding third set, Elmer Moller lost his second service game, and after being broken for the second time in the set while trailing 2-4, Dodig served out the match to secure the tournament victory.