Russian Medvedev, who had been booed for his antics against Fritz, put his fingers in his ears after sealing victory against De Minaur.
He lost only nine points on his serve as he wrapped up the win in an hour and 18 minutes.
“I went into this match blocking the noise, even from myself,” said 2020 champion Medvedev, 28.
“I really didn’t care what was happening on the court, I just tried to play, and it was a good feeling.”
Medvedev’s temperament was under scrutiny after his surly behaviour 48 hours earlier but he struck the ball superbly and broke in the third game with a cross-court winner.
He gained a double break when De Minaur double-faulted, and went on to take the first set in 40 minutes.
De Minaur, 25, battled in a pulsating second set but Medvedev’s stunning backhand put him 5-4 ahead and he held serve to clinch victory.
In the doubles, Patten and Heliovaara beat Australians Max Purcell and Jordan Thompson 7-6 (7-3) 7-5 in a repeat outcome to their Wimbledon final.
The British-Finnish duo are bidding to become the first team to capture the Wimbledon and ATP Finals trophy in the same season since Mike Bryan and Jack Sock in 2018.
