Medvedev, who is set to be the top seed at this month’s Australian Open with Novak Djokovic facing deportation over a visa issue, was dominant in the first set.
But the gritty big-serving Italian battled back to win a second set tie-break before the Russian got a crucial break in game three of the third set to carve out a 6-2, 6-7 (5-7), 6-4 win.
Russian No 2 Roman Safiullin earlier lost 7-6 (8/6), 6-3 to world No 10 Jannik Sinner with the tie forced into a doubles shoot-out.
Medvedev played just five doubles matches in 2021, but has fronted up for three so far in Sydney and partnered with Safiullin again to keep their unbeaten record intact, digging deep to beat Berrettini and Sinner 5-7, 6-4, 10-5.
“What we did amazing today was we were in a tough position at one point, and every change, every shot we had to make we tried to discuss it, and it worked,” said Medvedev of the doubles.
“Roman stated playing unbelievable and we had some crazy rallies, it was amazing.”
Medvedev and Berrettini met in singles for the first time since the 2021 ATP Cup final when the Russian ran out a 6-4, 6-2 winner to seal the trophy for his team, and he again had the edge.
Known on tour as “Deep Court Daniil”, he took up his customary position near the back wall to return serve, breaking twice in the first set.
The match turned in the third set when Medvedev’s service return earned him three break points to establish a 2-1 lead. He held serve for 3-1 and there was no way back for the Italian.
“I made some bad decisions in the second set so I tried to learn from that in the third. I served well throughout the match and that helped me,” added Medvedev, who led the ATP Tour with 63 match wins last year.
The Roberto Bautista Agut-led Spain and Hubert Hurkacz’s Poland have already made the last four and play each other Friday.
The fate of the final group rests on what happens Thursday evening.
If Alexander Zverev’s Germany beat Canada then Britain will become the last semifinalist. But if Canada win they will go through at Britain’s expense.
Britain keep their hopes alive by toppling the US 2-1.
In-form Dan Evans silenced big-serving American John Isner 6-4, 7-6 (7/3) to put his country in the driving seat, handing teammate Cameron Norrie an opportunity to close out the tie against Taylor Fritz.
But the world No 12 failed to do so, crashing 7-6 (7/4), 3-6, 6-1.
Fritz returned to partner with Isner for the decisive doubles, but they couldn’t conquer Evans and Jamie Murray who came through 6-7 (3/7), 7-5, 10-8.