The 29-year-old prevailed 7-6 (7-3) 6-7 (1-7) 6-4 over the second seed in the semi-final of the Wimbledon warm-up in Germany.
Medvedev had the only break point of the first set but failed to take it, only to fly through the tie-break and seize the initiative.
The Russian third seed, who now bosses the head-to-heads over the German 13-7, went 2-0 up in the second set but saw the home favourite hit back.
Medvedev steadied himself but Zverev, who had been ill again in his quarter-final, then dominated the second set tie-break.
Medvedev then broke for 2-1 in the decider and wrapped up a final showdown with Alexander Bublik — who beat top-ranked Jannik Sinner in the second round — in Sunday's final.
Bublik, the 2023 champion, fired 18 aces as he defeated Karen Khachanov 4-6 7-6 (7-5) 6-4 in the later semifinal on Saturday.
"I am happy with my level, I played great," Medvedev said.
"I could have done much better when I had the break in the second but it is normal. The same happened in the third set that when I had the break, he started playing better, returning better.
"I am happy that in the third set I managed to stay more composed and managed to save those break points. I would have loved to finish on the match points [in the second set].
"The first one I went for it and missed it. The second one I went a bit slower to wait for a mistake and he made a great point. I am happy to win in the end."
Zverev has again flattered to deceive this year with Munich his only tournament victory. He lost the Australian Open final to Jannik Sinner and went out in the last eight at the French Open.
The world No.3 heads to Wimbledon, which begins on June 30 - the third grand slam of the season - in mixed form as he seeks a first major singles title.
Medvedev, the 2021 US Open champion, has twice reached the semi-finals at the All England Club and is again looking strong on grass.
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