Sinner's victory over De Minaur was perhaps unsurprising – he had won all eight of their previous meetings, including a 6-3, 6-0 victory in last year's Davis Cup exhibition game.
The Italian was dominant in the first set, using all his loose strength to push past De Minaur and bring his team within touching distance of the final.
The second set was more competitive but De Minaur, who stayed in touch at 4-4, was the first to blink and Sinner promptly played out the match to the delight of the crowd.
Sinner has now won the last 24 sets he has played on the ATP Tour and has not lost a single one since the second round of the Shanghai Masters in early October.
“I had one of the best feelings ever last year when I won the Davis Cup,” said Sinner, who won the Australian Open and US Open this year. “We are happy to be in the final again.”
Berrettini could have made his own game easier if he had taken his chances in the first set against Kokkinakis.
The hard-hitting Italian secured the set with a lead of 6-5 and had a set point, but a shaky forehand forced him into the tiebreak.
Berrettini again had two set points on the break but was unable to convert them and Kokkinakis was rewarded for his hard work as he secured the first set.
Kokkinakis faced break points early in the second set, but Berrettini held firm, firing three huge serves to hold and taking advantage of his opponent's nervousness to force a decider.
The third set was once again a close affair before a superb forehand from Berrettini changed the momentum at 5-5 after Kokkinakis' serve.
Two errors from Kokkinakis gave Berrettini the decisive break that gave his team the perfect start.
