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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 here on Sunday.
Simon saved five match points before finally succumbing.
A distraught Simon said: "By a long way that was the most difficult defeat to accept of my entire career.
"What disappointment, it was a very important match for everyone. I had to win it, but didn't.
"I did the best I could, the only thing I can pick myself up on was that I wasn't better than I was.
"All I wanted to do was win - for me, for the others, for Jo (Tsonga) who didn't desefve to lose after winning two matches."
Berlocq reflected: "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 1hr 42mins 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.
On Friday, Tsonga had beaten Berlocq before Monaco came through victorious in his clash with Simon.
Argentina will face defending champions Czech Republic after they eliminated Kazakhstan earlier in the day.
Canada lead Italy 2-1 while Serbia hold the same advantage over the USA in the remaining last eight matchups.