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In a meeting between the two most successful nations in the tournament’s history, American world number four Taylor Fritz defeated Alex de Minaur, after Ben Shelton lost to Thanasi Kokkinakis to force a deciding match.
But Matthew Ebden and Jordan Thompson sent Australia, runners-up in the past two editions, through to the last four with a straight-set win over Shelton and Tommy Paul.
In a thrilling opening contest, Kokkinakis saved four match points to edge a 30-point third-set tie-break against Shelton, putting Australia ahead with a 6-1 4-6 7-6 (16-14) victory after two hours and 17 minutes in Malaga.
Fritz, who rose into the world’s top four after finishing runner-up to Sinner at last week’s ATP Finals, responded with a clinical 6-3 6-4 win against the ninth-ranked De Minaur to force a decider.
However, Ebden and Thompson proved too strong for Paul and Shelton in the doubles match and completed an efficient 6-4 6-4 win with a break of serve in both sets.
That sent 28-time champions Australia into the nation’s third successive Davis Cup semi-final and the pair celebrated with a chest bump before embracing team captain Lleyton Hewitt – winner of two Grand Slam singles titles.
Hewitt, part of Australia’s last triumphant Davis Cup team in 2003, said: “We’ve got a rich history in this competition. These boys know it’s a great honour every time you get the chance to wear the green and gold out here.
“We’ve had a group of six guys that have really put their hands up the last three or four years now. They’ve gelled together well and I’m just super proud of the whole team as a collective.”