Inspired captaincy, a nerve-shredding underdog's win for Thanasi Kokkinakis and good old-fashioned Australian doubles pedigree has powered Australia to a shock 2-1 win over the USA and into the semi-finals of the Davis Cup in Spain.

Lleyton Hewitt outduelled his American counterpart Bob Bryan in the key captaincy calls of their quarter-final tie in Malaga on Thursday as 28-times winners Australia defeated the 32-time champs in the battle between the two most successful nations in the historic men's 'World Cup of tennis'.

First, Hewitt plumped for the daring choice of world No.77 Kokkinakis to open proceedings against big-hitting left-hander Ben Shelton, ranked 56 places higher, and the Aussie outsider came up trumps after saving four match points to prevail in an epic deciding tiebreaker 6-1 4-6 7-6 (16-14).

Then, after Alex de Minaur was blown away 6-4 6-4 by Taylor Fritz in the No1s' duel, it was down to doubles grand slam winners Jordan Thompson and Matt Ebden to team up for the first time in the Cup and defeat Shelton and Tommy Paul 6-4 6-4 in the deciding rubber.

"Incredible. When we got the break there at four-all, I could have run over the top of the whole bench," beamed Thompson. "I was wearing my heart on my sleeve, you know, bleeding green and gold."

The American skipper Bryan had ditched his specialist doubles pair, Olympic silver nedallists Rajeev Ram and Austin Krajicek, trying to shake up the Aussies by unleashing two of his singles stars - but the decision backfired spectacularly.

"We were hoping to catch the Aussies a little bit by surprise," sighed Bryan, to which Hewitt countered: "It didn't surprise us that much, to be honest ... I'd seen them do drills during the week..."

It put Australia one triumph away from a third-straight final appearance after two runner's-up finishes, but they'll have to topple either champions Italy or Argentina on Saturday (Sunday AEDT) to earn another crack at lifting the Cup for the first time in 21 years on Sunday (Monday AEDT).

"I don't know if I've been that pumped up in my life. I wanted that for my team," said Kokkinakis, after finally prevailing on his seventh match point in the marathon 30-point breaker.

"It could have gone either way, but I kept my nerve."

Hewitt reckoned it hadn't been a gamble to play Kokkinakis, even though he'd only played one lower-level Challenger in Sydney and a losing Laver Cup singles in the two months since two big wins at the Davis Cup qualifiers in Valencia.

The much higher-ranked Montreal Masters winner Alexei Popyrin and Thompson were both overlooked, with Hewitt grinning: "He (Kokkinakis) played like the winner of the New South Wales Open Challenger about a month ago!

"Obviously, never easy making these decisions but we know if we can get him going out there and playing his highest level, he's dangerous for anybody, I don't care who it is. I had full belief in him.

"We kind of put him on ice, pretty much until now, and let him off the leash today, and he fully repaid us."

Belief amply rewarded, Hewitt then thrust a disappointingly flat de Minaur into the second singles for a rematch with world No.4 Fritz, who had only just pipped him at the ATP Finals the previous week.

The key moment came as Bryan revealed his doubles switch 15 minutes before they were due to go on court.

"We were expecting the other pair and but we knew they've got incredible players who can play doubles, so we were ready," said Ebden, who like Thompson has won grand slam doubles but both with a different partner, Purcell, who was cheering on at courtside after recent injury struggles. "What a day!..."