The 28-year-old American eliminated Vukic 6-2, 4-6, 7-6 (7/3) after two hours and five minutes in the grass-court event at Newport, Rhode Island.
"The match had a lot of ups and downs. Third set I really caught a good rhythm and that energized me," Eubanks said.
"After I got that first hold in the third set I felt like myself again. I was enjoying it. I was really pleased with how I played and how I competed. Excited to get another win."
Eubanks, who won his only prior ATP final on Mallorca grass in June 2023, advanced to a Saturday semi-final against the winner of a later match between Aussie qualifier Alex Bolt and US second seed Marcos Giron.
Eubanks, ranked 128th, was only 6-15 in ATP matches this year until his Newport run.
Vukic, 8-1 this year in deciding-set tiebreakers, surrendered a double fault to give Eubanks a 4-2 lead and Eubanks followed with a forehard winner.
They exchanged errant forehands before the sixth-seeded Aussie netted a forehand volley to hand fourth-seeded Eubanks the triumph.
Vukic reached his only ATP final last July in Atlanta, losing to American Taylor Fritz.
Saturday's other semi-final will send US wild card Reilly Opelka, in his first tournament since 2022 in Washington, against 19-year-old countryman Alex Michelsen, last year's Newport runner-up.
Opelka, at 1,188th in the world, is the lowest-ranked player in the ATP era to reach a semi-final, having tumbled during his absence following hip and wrist operations.
