In a 6-7(7), 6-4, 6-2 victory at the Abierto Mexicano Telcel, the Danish player won eight of the final 10 games to close out a match that hung on a knife edge until late.
World No 2 Casper Ruud made a perfect start to his Australian Open campaign, defeating Czech Tomas Machac 6-3, 7-6(6), 6-7(5), 6-3 to reach the second round in Melbourne with his eyes set at the top spot in the ATP rankings on Tuesday.
Berrettini got the better of World No 3 in a much-anticipated match, winning it 6-4, 6-4 in straight sets to seal Italy's victory over Norway and take a commanding 3-0 lead. The Italian team will face either Poland or Switzerland in the City Finals on Wednesday.
Norway started Sunday's United Cup match against Brazil trailing 2-0. Despite World No 3 Casper Ruud keeping Norway's hopes alive, the country was unable to fight its way back.
The Serbian's high-quality return game proved to be a huge difference between both players. He carved out all five break-point opportunities in the match. Ruud also hit strongly, but the 'Big Match Djokovic' was too good for him in this 93-minute battle for the title
The sixth seed clinched a 3-6, 6-3, 6-2 win over the Greek to set up a clash with Casper Ruud in semifinals. Though Rublev was one set down, his groundstrokes helped him clinch his 51st tour-level win of the season.
The third seed clinched a 6-3, 4-6, 7-6(6) win over the American to confirm his progression from Green Group. Coming into the match after a win over Canada's Felix Auger-Aliassime, Ruud managed to hold his calm to clinch the semifinal spot after a tense battle of two-hours and 12 minutes
The current world number 1 Carlos Alcaraz of Spain will be missing the tournament due to an injury. This will leave Nadal, Djokovic, Stefanos Tsitsipas, Casper Ruud, Daniil Medvedev, Felix Auger-Aliassime, Andrey Rublev and Taylor Fritz fighting for the singles title