Zeballos, playing in his first ATP final, led 3-0 in the second-set tiebreaker but allowed 93rd-ranked Stakhovsky to reel off six straight points, winning it 10-8 to level the match.
Stakhovsky, whose first title came last year in Zagreb, broke for a 4-3 lead in the third set and had a match point in the ninth game but Zeballos held before breaking back.
In the deciding tiebreak, both players held match points before the 23-year-old Kiev native finally sealed victory 9-7.
"I must say I was a bit lucky today because my opponent played better than me," Stakhovsky told a news conference.
"I was also getting tired in the second set as I had to play eight matches, including three qualifiers, here," added the Ukrainian, who beat former world number one Marat Safin in the semi-finals on Saturday.
"Yesterday's match took a lot out of myself, but somehow today I was able to find enough energy in key moments."
Zeballos was satisfied with his performance in St Petersburg.
"Overall, I can't be too disappointed because here I reached my first (ATP) final," said the 24-year-old from Buenos Aires.
"In the final I had my chances. I had a lot of break points but he played really well on key points." (Reporting by Boris Khodorovsky; writing by Gennady Fyodorov; Editing by Ed osmond, To query or comment on this story email sportsfeedback@thomsonreuters.com)
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