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“I really didn’t care what was happening on the court, I just tried to play, and it was a good feeling.
“The more popular you become, the more fans you get, the more haters you get, the more attention you get. Sometimes even the good noise can make you off balance.
“You win everything and people say you’re a god. You lose two matches and people say ‘Your career is finished.’ Sometimes it’s good to just block it.”
Australian De Minaur will be knocked out with a match to spare if the other tie in the Ilie Nastase Group between Italian top seed Jannik Sinner and Fritz goes to three sets later on Tuesday (19:30 GMT).
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.
Meanwhile, Britain’s Henry Patten and partner Harri Helioevaara are on the brink of the doubles semi-finals after a second straight triumph.
They 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.