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.