The second seed from Ukraine eventually came through a 6-7 (7-9) 6-4 6-1 winner after a rain-affected final.
German fourth seed Haas was leading 6-5 in the first set when the players, having previously left the court due to a light shower after the ninth game, were forced off again, this time by heavy rainfall.
When they returned, Haas took the first set, but world No.25 Dolgopolov capitalised on one of his five break points in the second set to level the match up before he claimed victory with two breaks in the deciding set.
The title is 23-year-old Dolgopolov's second ATP World Tour crown following his win in Umag last year, while the 34-year-old Haas, having reached a third final in five tournaments, had been chasing the 14th title of his career.
Dolgopolov said: "For sure, I'm very happy, and especially winning a match like that [which is] really tight, goes up and down, the rain breaks. I'm really happy with myself that I stayed concentrated and was in the match in all the three sets. I'm just happy to win."
Haas admitted feeling frustrated but is also delighted with the bigger picture that is his recent form.
"Not only here, but I've proven [myself] a couple months ago winning a title in Halle and getting to a final in Hamburg two weeks ago and getting to a final here. It's been unbelievable.
"Obviously I'm a little bit frustrated right now still. I thought I had some chances to win this title and I really wanted it. It's always tough to lose, even when you had a great week, but you just have to let it sink in and overall, I'm really proud to get here to a final and play really solid tennis. I just hope I can stay injury-free and keep going and try to keep it moving."
Meanwhile, Briton Dominic Inglot won his first ATP doubles title in Washington on Sunday.
Teaming up with Filipino Treat Huey, Inglot recorded a 7-6 (9/7) 6-7 (9/11) 10-5 victory over the big-serving pair of Kevin Anderson and Sam Querrey.
Inglot said: "I feel really happy. We played a high level of tennis. They played a really good level as well. It's good to know that we're able to compete with these kinds of guys and we kept on in the final as well, and I'm really happy we're able to win our first tournament in Washington."