The two-time winners will face Netherlands in Sunday's showpiece after the Dutch ousted Germany 2-0 on Friday to make the final for the first time in 104 years of trying.
Sinner, who has never lost against De Minaur in nine matches including last year's Davis Cup final, triumphed 6-3, 6-4 in Malaga.
In the first singles rubber Matteo Berrettini earned a 6-7 (6/8), 6-3, 7-5 win over Australia's Thanasi Kokkinakis in two hours 46 minutes.
"Finals are a huge privilege to be a part of -- Sunday is a final and I'm very happy to be here in this position," said Sinner.
"Winning would mean so much for us, not only for the win but because it would mean we defended our title.
"If we don't, it's still an amazing achievement, we showed it was not lucky last year, we're here because we are an amazing team."
Australia, beaten finalists in each of the last two years, are the second most successful team in the tournament's history with 28 titles but last won it in 2003.
Australian Open, US Open and ATP Finals winner Sinner is enjoying a superb year and can cap it with another Davis Cup triumph.
The 23-year-old is still waiting for the outcome of the World Anti-Doping Agency's appeal against his initial exoneration for twice testing positive for traces of the steroid clostebol in March.
However he has not been distracted and despite De Minaur, ranked ninth, battling hard, claimed the first set without much stress.
The players exchanged breaks in the second and third games before Sinner broke decisively for a 4-2 lead with a delicious drop shot, and he served it out.
The Italian worked the first break points of the second set in the ninth game. De Minaur saved two but Sinner converted the third with a passing shot to serve for the match.
Sinner claimed victory when De Minaur returned badly wide and mangled his racquet in sheer frustration.
"He hasn't won a million matches this year for no reason -- it was tough," admitted De Minaur.
"It's like trying to solve a puzzle that not a lot of people have managed to solve.
"His ball speed, his consistency, it feels like there's no real let down of focus throughout the whole match."
'Take bid seriously'
Berrettini was superb in the doubles decider as Italy beat Argentina in the quarter-finals and captain Filippo Volandri rewarded him with selection in the opening clash in place of Lorenzo Musetti.
Berrettini watched on as Italy won the Davis Cup for the first time in 47 years in 2023, not part of the squad but cheering from the sidelines as he recovered from an ankle injury.
This year he has been able to play an important role in Italy's charge towards the final.
"After I lost the first set it wasn't easy to digest that, but when I'm fighting for my country with this crowd... I kept on fighting," said Berrettini.
Kokkinakis clung on to take the first set to a tie-break which he shaded.
Berrettini claimed the second with a break in the eighth game, which he served out.
Kokkinakis survived two break points in the first game of the third set and no others emerged in an even battle until the 11th game when he conceded two more.
Berrettini capitalised on the first and clinched the set with an ace to delight thousands of Italian supporters at the Martin Carpena arena.
"I felt I was playing an away tie, it was tough on Australia -- we were playing in Spain but I thought we were in Italy," said Kokkinakis, echoing prior Australian complaints about the revamped Davis Cup format.
"Once again we're a long way from Australia aren't we?" said captain Lleyton Hewitt.
"It will be nice when they take our bid seriously to host the finals, Australia will put on a bloody good event."
