The Australian and US Open champ then confirmed his dominance after breaking again to lead 5-4 and serving out to wrap up a ninth straight win over the Sydneysider just under a fortnight since he also outplayed de Minaur in the ATP Finals.
“Hopefully, this can give us confidence for tomorrow,” said Sinner.
Kokkinakis, who had been instrumental in giving Australia an early lead in their quarter-final victory over USA on Friday when he overcame big-serving Ben Shelton, was again charged with getting them off to a flyer.
Skipper Hewitt again plumped for the 28-year-old against the Americans ahead of the higher-ranked Alexei Popyrin and Jordan Thompson.
And the world No.77 nearly delivered again before narrowly losing out 6-7 (6-8) 6-3 7-5.
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Kokkinakis, fresh off winning the NSW Open’s ATP Challenger Tour event in Sydney, showed he meant business in a see-saw first set before edging a nervy tie-break 8-6 after Berrettini had contrived to blow three set points.
But backed by vociferous Italian support, Berrettini fought back with some sublime power hitting to level the match and taking the second set 6-3.
And after Kokkinakis finally cracked when suffering a crucial service break at 5-5 in the decider, Berrettini held firm to serve out the match.
“We’re in Spain,” Kokkinakis said, “but it felt like we were in Italy.
“It was a tough match. He served incredible. 89 per cent in the third set and it didn’t give me much of a chance to look in.
“I regret a game I played in the second set where I lost a little bit of focus to get broken. I lost my concentration for a little bit in the third set.”
Meanwhile, de Minaur was left sighing after yet another straightforward Sinner triumph.
“Well, it’s like trying to solve a puzzle that not a lot of people have managed to solve,” he shrugged.
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“That’s probably the best way I would describe it.”
“It feels like he comes out, he’s solid, he plays well. In the big moments he steps it up.
“He’s just a very tough player to play against this year, as many other opponents have definitely felt that.”
With Sinner in this mood straight after his season-ending ATP Finals triumph in Turin, the champions will now be hot favourites to defend their crown after the Dutch claimed a shock victory over Germany in Friday’s first semi-final.
AAP