Second-seeded Dolgopolov dropped the first set in a tiebreaker but ultimately prevailed over the fourth-seeded Haas 6-7 (7-5), 6-4, 6-1.
Play was interrupted briefly late in the first set, then was stopped for a longer time before the tiebreaker due to heavy rainfall.
The contest was delayed nearly 3 hours in total.
The 23-year-old Dolgopolov improved to 2-2 in finals after winning last year at Umag.
Haas, meanwhile, fell to 13-11 all-time in title matches while appearing in his third final in five tournaments. He bested Roger Federer in the Halle final in June.
Britney Spears debuts 'Perfume' video
Video of Victoria’s Secret models trying to 'twerk' hits Instagram