Bublik had lost his previous six meetings against Russian Medvedev, winning only one set in the process, but produced a superb exhibition of grass-court tennis to end that streak on Sunday.
Former world No.1 Medvedev has now lost his last six Tour-level finals.
So often the showman, Bublik, fresh from his run to the quarter-finals in the French Open, showed his new maturity with a calm display in the final as he continued the form that saw him beat world No.1 Jannik Sinner in the last-16 this week.
The 27-year-old broke the Medvedev serve in the eighth game of the first set and then held his own with ease to move ahead during an incredible 12-point winning streak.
Medvedev had a set point when Bublik served at 4-5 in the second set but could do nothing as his wily opponent feathered a delicate drop shot from behind the baseline.
Third seed Medvedev then led 4-1 in the tiebreaker but the unseeded Bublik stormed back to complete a memorable week and repeat his 2023 title run on the German grass.
"I had such tough months since last Wimbledon to probably this summer," said Bublik, who was outside the top 75 as recently as last month but will rise to 30 on Monday.
"I was close to calling it quits after Wimbledon because I was not enjoying it any more. Now this is happening. I don't know. Quarters at the French? Winner here? I have no words.
"I have never beaten Daniil. He's a super tough player to play, especially with my style, and today everything clicked in mentally and physically. That's one of the wins of my career."
