The 20-year-old Tsitsipas tossed his racket in the air and put both hands to his head when Gulbis put a forehand into the net after 1 hour, 21 minutes.
Tsitsipas had lost his previous two finals, both times to Rafael Nadal. The No. 145-ranked Gulbis was an easier proposition, though, and Tsitsipas won 80 percent of his service points and didn't have his serve broken.
"Of course I feel happy because I'm the first Greek (to win an ATP title)," said 16th-ranked Tsitsipas, who became the 12th first-time title-winner on the ATP Tour this year. "Hopefully many Greek players can achieve something like this. I would be super-happy to see them achieve something like this in the future."
Gulbis had won all six of his finals at ATP tournaments. This was his first since 2014, having beaten top-seeded John Isner in the semifinals.
It was still a great week for Gulbis, who only had four tour-level wins this season before coming to the Swedish capital.
"He played a really good match. He had a great week," Gulbis said. "I know it's a big deal to win your first ATP title, so enjoy it. I wish that it's not the last one."
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