The world number 11 came through 7-6(3), 6-7(3), 6-4 after an exceptional baseline battle lasting just under three hours.
On Sunday, Medvedev will play in his first final on the Tour since March 2024, against Kazakhstan's Alexander Bublik, who later beat Russian Karen Khachanov 4-6, 7-6, 6-4 in the second semi-final.
It was the 20th clash between two players of the same generation, with Medvedev, 29, now leading 28-year-old Zverev 13-7.
A finalist in Stuttgart last week, Zverev had been hoping to go one better on the grass of Halle after being a losing finalist at the tournament in 2016 and 2017.
But former world number one Medvedev once again proved a tough opponent for the second seed, having won 12 of their last 14 duels, the last in the semi-finals of the Australian Open at the end of January 2024.
The 2021 US Open winner and two-time Wimbledon semi-finalist in 2023 and 2024, Medvedev squandered a break lead 2-0 and three early match points on Zverev's serve (6-5) in the second set.
Zverev led the tie-break 6-0, then 7-1 to extend the match into a third set dominated by Medvedev, who broke 2-1 and held his service game 3-1, saving four break points.
The third seed wrapped up the match with a forehand winner, sending him through to his second final in Halle, where he finished runner-up in 2022.
"I would have much preferred to finish when I had match points in the second set, but I'm happy to have won. I hope in the other semi-final they'll run a little, because I'm tired," joked the Russian.
For his 21st tour title, his first since his triumph on the clay courts of Rome in May 2023, Medvedev will challenge 2023 Halle winner Bublik, ranked 45, who claimed the scalp of world number one Jannik Sinner in the second round.
Big-serving Bublik took just over two hours to get past 22nd-ranked Khachanov, firing 19 aces, and taking the tie on his fourth match point.
The 28-year-old Kazakh is bidding for his fifth title after Montpellier in 2022 and 2024 and Antwerp and Halle in 2023.