The Russian, who said he was looking forward to the season being over after succumbing to a tantrum during his opening round defeat to Taylor Fritz, brushed aside the Australian No.1 6-2 6-4 in 78 minutes of high-octane tennis.
De Minaur did not play badly, he was simply barely allowed to play at all with Medvedev hitting 24 winners and dropping two points on serve in the second set.
Daniil Medvedev 'blocks out the noise' after beating Alex de Minaur at the ATP Finals in Turin. (AP PHOTO)
The Sydneysider now needs to beat Fritz heavily in the last round-robin game, and hope Medvedev also loses by a big margin to Jannik Sinner, to have any hope of progressing. But if the American even takes a set off Sinner in Tuesday's late match the Australian, who has already lost to Sinner, will be out.
Medvedev was beaten by Alexei Popyrin in the Paris Masters last month but in Turin he showed why he is fourth in the world.
With de Minaur still to regain full movement after his hip injury he was unable to counter the Russian's mastery of angles.
The Australian had won the pair's only previous match this year, in the last 16 at Roland Garros, but that counted for little when his opponent began as if determined to exorcise the memory of his opening match.
He suffered a meltdown when losing to Fritz, being deducted a point for hurling his racquet and damaging a courtside microphone. This after he had already destroyed one racquet as he railed in frustration.
After that loss Medvedev said he had taken "zero pleasure of being on the court" for "a long time", but he will have enjoyed the opening set even if his countenance remained a mask of concentration.
This was a highly focused Medvedev, and he seized the first set in 40 minutes. De Minaur survived a break point in the first match but was broken in the third and fifth to find himself 5-1 down in barely half-an-hour. Although he then held to love to restore some confidence Medvedev served out comfortably.
De Minaur held to love again to start the second set which went with serve until the ninth game when a superb backhand winner secured Medvedev the break. Serving for the match he made no mistake.
At the end he put his fingers in his ears before writing 'block the noise' on a camera lens. He subsequently said he went into the match telling himself whatever happened there was a positive ending; either he was heading home for a break after his final group match or would still be in contention.
Barring an improbable run of results de Minaur's focus will soon turn to Australia's Davis Cup challenge in Malaga next week.
He can reflect on a successful 2024 in which he reached the quarter-finals in the last three grand slams, consolidating a top ten place, despite the hip injury suffered at Wimbledon that kept him off court until the US Open.
In the other group the further participation of Carlos Alcaraz, who lost his first match to Casper Ruud, is in doubt. The 21-year-old cut short his practice session after five minutes as a chest complaint was making breathing difficult. He is due to play Andrey Rublev on Wednesday.
Earlier Max Purcell and Jordan Thompson lost 7-6 (7-3) 7-5 to Harri Helioevaara and Henry Patten in the doubles and are 1-1 after their two matches, still in with a reasonable chance of making the last four.
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