Duckworth had rattled off five victories in seven days after progressing through qualifying and later knocking out the No.7 seed Gabriel Diallo, of Canada, and then defeating Italian No.3 seed – and world No.22 – Flavio Cobolli.
On Saturday, he went toe-to-toe with No.2 seed Medvedev, winning a gripping tiebreaker to take the first set, before the Russian came back to win 6-7 (8-10) 6-3 6-2.
Duckworth reached the final in Almaty four years ago but his age (33), injury record and world ranking (No.138) suggested a repeat was improbable.
Medvedev, who had won their only other meeting, admitted he was pleased to win after being pushed so hard by Duckworth.
"I think the level was incredible today, from both me and my opponent.
"In the tie-break, I could have played better, but it happens. Throughout the match, there were some amazing points from both of us, so I'm really happy to be able to win this match."
Duckworth's superb week moved him up to No.108 on the ATP live rankings.
Medvedev has had a turbulent year, including a big fine for a meltdown during defeat in the first round at the US Open, and he is aiming to win his first tour-level title since Rome in 2023.
His form has picked up in recent weeks though, and by reaching his 40th tour-level final, he has become the second active male player after Novak Djokovic (143) to achieve that feat.
In Sunday's final he will face France's Corentin Moutet, the No.8 seed, who beat Alex Michelsen of the US in straight sets.
