Argentina are into the Davis Cup World Group semi-final after their world number 71 Carlos Berlocq beat 13th-ranked Frenchman Gilles Simon to hand the South Americans a 3-2 win on Sunday.
A distraught Simon, who saved five match points before finally succumbing, said it was the lowest point of his tennis career.
"By a long way that was the most difficult defeat to accept of my entire career," he said.
"What disappointment, it was a very important match for everyone. I had to win it, but didn't.
"I did the best I could.
"All I wanted to do was win -- for me, for the others, for Jo (Tsonga) who didn't deserve to lose after winning two matches."
Argentina will face defending champions Czech Republic after they eliminated Kazakhstan earlier in the day. Serbia and semi-final newcomer Canada also won their quarter-finals on Sunday.
Berlocq said he didn't want to let down his family, friends and teammates who were pulling for an Argentina victory at the Parque Roca in Buenos Aires.
"When you are in your own country, with everyone around, your family, your friends, who have confidence in you, their confidence is contagious.
"All the team believed victory was possible. It was a battle, fortunately we won it."
France had levelled the quarter-final tie earlier after Jo-Wilfried Tsonga dismantled Juan Monaco 6-3, 6-3, 6-0 in one hour, 42 minutes to force a deciding rubber.
Against the odds, that went to Berlocq, who fought back to prevail 6-4, 5-7, 7-5, 6-4 against Simon who was called in late to replace Richard Gasquet.
David Nalbandian and Horacio Zeballos had also come from behind to win Saturday's doubles, which gave the hosts the upper hand going into the final day.
World No. 1 and Australian Open champion Novak Djokovic's victory over Sam Querrey of the United States on Sunday advanced Serbia into the semi-finals.
Djokovic, who had to battle through an ankle injury he suffered in the opening set, earned a 7-5, 6-7 (4/7), 6-1, 6-0 win to give the Serbians an insurmountable 3-1 lead in the best-of-five tie.
It is the second win for Serbia in four years over the 32-time titlist USA. In their only other previous Davis Cup encounter Serbia defeated the Americans in Belgrade in 2010.
"I am sorry for team USA but it was a thrilling weekend for all of us," Djokovic said.
Djokovic had to play through the pain of a bad right ankle, which he sprained in the third game of the opening set.
"I took some anti-inflammatories, and they kicked in at the end of the second set," he said.
Djokovic said he probably wouldn't have finished the match if it wasn't Davis Cup.
"If I wasn't playing for Serbia and didn't have my team watching me, I don't know if I would have continued," he said.
The 25-year-old Djokovic clinched the victory over world number 20 Querrey with a backhand winner, ending the two hour, 35 minute match.
Serbia will now meet Canada after Milos Raonic sent the Canucks to their first-ever semi-final by beating Andreas Seppi of Italy 6-4, 6-4, 3-6, 7-5.
The 22-year-old Raonic overpowered Seppi with his booming serve before Seppi stepped up and won the third set in Vancouver, British Columbia.
But Raonic rebounded to win the fourth, finishing the match with 35 aces to complete the historic win for Canada, who will travel to Serbia for the semi-finals in September.
Lukas Rosol of Czech Republic put the defending champions into the semi-finals with a tough win over Kazakhstan's Evgeny Korolev at Astana.
Rosol, who is 63rd in the ATP rankings, won 7-6, 6-7, 7-6, 6-2 in his first ever head-to-head meeting with the 25-year-old Korolev to give his team an unassailable 3-1 lead in the tie.