Trailing 2-0 on Friday after defeats for Andy Murray and Kyle Edmund, the chances of Leon Smith’s team reaching a second successive final looked very slim indeed.
But the Murray brothers won the doubles rubber on Saturday and Andy defied a leg injury to defeat Guido Pella 6-3, 6-2, 6-3 in the opening match on Sunday.
That meant the tie came down to a clash between Dan Evans and Leonardo Mayer, and it was the Argentinian who prevailed 4-6, 6-3, 6-2, 6-4.
Evans would have expected to face Juan Martin del Potro, conqueror of Murray in five hours on Friday, but the former US Open champion hinted on Saturday he was not prepared to risk his fragile body.
Del Potro has twice spent long periods on the sidelines because of wrist problems, only returning from nearly two years out in February.
It made the decision to play him alongside Mayer in the doubles, a rubber they were never favourites to win, even less fathomable.
Murray said of Del Potro’s absence: “I’m surprised but it’s understandable. He’s had so many injury problems that everyone’s just forgetting about.
“He’s hardly played tennis for the last three years and he knows his body. His decision 100 per cent should be respected.”
In the end it was not a situation Argentina were made to regret as Mayer, ranked a lowly 114, produced a powerful and impressive performance to send his country through to a final clash with Croatia in November.
Evans is at a career-high ranking of 53, so could have been considered the favourite on paper, but Mayer was as high as 21 last season before injury problems and had won his last seven Davis Cup singles matches.
One of those, against Brazil’s Joao Souza last year, was, at six hours and 42 minutes, the longest singles rubber ever in the competition.
Meanwhile, for all his Davis Cup heroics, including winning deciding rubbers twice against Slovakia and Russia, none of Evans’ wins had come in the World Group.
The 26-year-old, who was preferred to Edmund following his disappointing performance against Pella, began well, but Mayer made a lot of errors in the opening set.
Once he cut those out and his big serve began to fire, Evans was in trouble and he could not change the momentum.
The result meant Murray’s efforts in dragging his body through the pain barrier were in vain.
After more than eight hours of tennis already in this tie and on the back of a gruelling summer, it was amazing he even had the energy to walk on to the court.
On the face of it, it was a straightforward victory against Pella, but he spent much of the third set wincing in pain after hurting his right thigh and needed an off-court injury time-out.
The Scot said: “I’ve never really had any muscle injuries before. That was worrying for me and thankfully I managed to get it done in straight sets. I was still moving okay, but when you get pain in your body it distracts you.”
Murray was off court for more than five minutes and lost only one game on the resumption, breaking the Pella serve twice.
The ethics of injury time-outs was a big topic at the US Open, with Johanna Konta recovering from an on-court collapse to beat Tsvetana Pironkova and then Novak Djokovic taking two in the final.
Murray said with trademark deadpan delivery: “The reason I had to go off is because I can’t get my nuts out on the court.
“But I would be annoyed for sure if that was me. Obviously I was in control of the match, but I then broke serve. If you’re the one that’s sitting and waiting, it’s frustrating.”
The Scot will now focus on resting his aching body and is hoping to be fit for his charity event in Glasgow on Wednesday, when he is due to play Grigor Dimitrov.
Murray, whose next tour event is in Beijing in two weeks’ time, was happy with how he handled the situation.
“This weekend I accepted it better than what I have in the past,” he said. “I expected to feel tired and I knew I was going to be in some pain.”