After initially taking the first set 6-1, De Minaur looked to be on course for a straight-set victory.
However, Medvedev managed to break in the seventh game to take a 4-3 advantage, before serving out the second set to win 6-4.
De Minaur through to last four in Sydney
The Russian then managed to take control of the match, racing ahead to a 4-0 lead, but 18-year-old De Minaur - the youngest player to make the Sydney Internationals since Lleyton Hewitt - fought back.
Winning four of the next five games, the plucky Australian was cheered on by his home crowd, but Medvedev, ranked 84th in the world, once more took control to serve out the set 7-5 and win the match, and his first ATP Tour title.
Earlier in the day, Angelique Kerber beat Ashleigh Barty to win the women's singles title 6-4, 6-4.
Zverev stuns Nadal to reach Madrid semi-finals