Argentina captain Martin Jaite's team went through to a semi-final away to holders Czech Republic, the nation that beat them in Buenos Aires at the same stage last year.
"It's definitely the best result of my career," Berlocq said.
World number eight Jo-Wilfried Tsonga had earlier bamboozled Juan Monaco 6-3 6-3 6-0 to bring France level at 2-2 and take the tie into the final rubber at Parque Roca.
"We knew victory was possible after Tsonga's great match. He didn't allow Monaco to express himself," France captain Arnaud Clement said after the match.
"[But] we have to be realistic about what happened this weekend. Argentina had a very well prepared team," he said.
"I'm disappointed, the players are disappointed and so are the whole team staff."
The 30-year-old journeyman Berlocq became an unlikely hero for Argentina in the absence of top 10 player Juan Martin del Potro.
Having given Tsonga a run for his money in a five-set defeat in Friday's opening singles, Berlocq made a mockery of the rankings as he took the first and third sets before running up a 5-2 lead in the fourth.
Simon put up some dogged resistance at the end, saving five match points total including a break of service before Berlocq clinched it on the sixth for Argentina's first win over France in six meetings.
"It was very hard, I had an adversary who was playing well and a crowd that didn't let up during four hours," Simon said referring to Argentina's passionate supporters.
"Argentina is lucky to have some of the best supporters in the world. The players can use the crowd [to lift them] when they're tired."
Tsonga was too good for Monaco, who had surprised with his win over Gilles Simon in Friday's second singles after a dismal start to the season.
Breaking Monaco in the Argentine's first service game was enough for Tsonga to cruise to the first set and two more breaks gave him the second after fine shot placing and positioning at the baseline before a superb lob to seal it.
The deciding set turned into a nightmare for Monaco, who failed to take a point in the opening three games and only one in the next as Tsonga broke him almost at will.
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