Great Britain missed out on the ATP Cup semi-finals after Jamie Murray and Joe Salisbury lost the decisive doubles rubber against Australia despite having four match points.
The 3-6 6-3 18-16 win for Nick Kyrgios and Alex de Minaur after a match tie-break gave the hosts a 2-1 win.
Dan Evans had earlier kept Britain in the tie with a thrilling three-set win over De Minaur.
Kyrgios had beaten Cameron Norrie in the opening singles in Sydney.
Australia will play Spain or Belgium on Saturday for a place in the final of the inaugural edition of the men's team tournament.
More knockout-stage heartbreak for GB
Fewer than seven weeks after the last men's team tennis event - the rival Davis Cup - Great Britain have once again suffered an agonisingly close defeat in the knockout stage following their semi-final loss to Spain that also came down to the doubles.
Murray will be left kicking himself over one squandered opportunity in particular - a terrible volley at the net - on Britain's second match point at 11-10 in the decider.
With almost the whole court at his disposal, the Scot somehow overcooked his shot and put his hands on his head in disbelief.
Instead it was Australia celebrating a few points later when Salisbury sent a backhand long on the hosts' fifth match point.
Kyrgios carried De Minaur over his shoulder after they hugged on the ground and the home cheers rang out.
De Minaur and Kyrgios had not even meant to be playing in the doubles but were brought in instead of Chris Guccione and John Peers in what captain Lleyton Hewitt said had been a "tough" decision.
While Kyrgios had breezed through his 6-2 6-2 singles win over Norrie in one hour 12 minutes, De Minaur, 20, spent nearly three and a half hours on court for his epic singles match against Evans before he was asked to play again.
"Nick was playing extremely well in singles and was pretty fresh, Alex is a hell of a doubles player," Hewitt said. "I thought I'd throw on a bit of firepower and it ended up paying off."
'Phenomenal' Evans delivers for Britain again
British number one Evans, who upset world number 11 David Goffin to inspire the turnaround against Belgium in the group stage that kept his team in the tournament, once again showed he has the mettle and the shots to beat higher ranked opponents.
He sealed a thrilling 7-6 (7-4) 4-6 7-6 (7-2) win in three hours 24 minutes - the longest match of the tournament.
The Briton, ranked 24 places below De Minaur at 42nd in the world, put behind him a poor start to break back in the fifth game and took the first set on a tie-break when his opponent netted.
The young Australian, who won three ATP titles last year, kept himself in the match by holding on to an early break to take the second set.
Evans had looked to be in charge of the third when he went 3-0 up but was then pegged back in what became an absorbing final set.
A time violation for Evans on his serve - given when it looked like he had already started his service motion - may have been playing on his mind to allow De Minaur a break back courtesy of a passing shot that was helped by the net cord.
Evans had four match points at 6-5 but a nerveless De Minaur saved them all with three emphatic winners and an ace to eventually force a tie-break.
With Kyrgios encouraging the home crowd to make even more noise with gestures from the bench, it was Evans who seemed to feed off the atmosphere, with a beautiful lob and stinging forehand winner at the net setting the tone as the Briton set up another four match points.
This time he converted without hesitation, wrapping up victory when De Minaur returned wide.
But De Minaur picked himself up from the loss to play an instrumental role in the doubles victory, where his constant threat at the net proved a menace for Britain.