The 21-year-old Indian pipped his higher-ranked rival 6-7 (13) 6-3 6-4 in the final, which could not be completed yesterday due to rain.
Yuki, ranked 277, was leading 4-2 in the final set yesterday when skies opened up and forced suspension of play.
Playing his second Challenger final of the season, the Indian youngster took the court today and held his nerves to emerge winner against a player, who was ranked 149 places above him.
The victory was a sweet revenge for Yuki as he had lost to Bradley, ranked 123, in July this year in Binghamton.
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Yuki had won his first singles title on the Challenger tour last year in Fergana, Uzbekistan.
In September, Yuki had ended runner-up to Chinese Taipei's Yen-Hsun Lu in the Kaohsiung event in Taiwan.
Yuki earned 80 ranking points and pocketed USD 7,200 as prize money for his effort.