Federico Delbonis swept aside Croatia's Ivo Karlovic 6-3, 6-4, 6-2 in the deciding rubber as Argentina clinched a first Davis Cup title with a stunning fightback in Zagreb.
Juan Martin del Potro, cheered on by Argentine football legend Diego Maradona, staged an incredible comeback from two sets down to beat Marin Cilic in the opening reverse singles to level the tie at 2-2.
Left-hander Delbonis then tamed the big-serving Karlovic as Argentina, runners-up on four previous occasions, became just the 15th country to lift the trophy in 116 years.
"This is one of those dreams that has come true," said Delbonis.
"I tried to keep focused to do what I had to do, that's all I could think because if I thought about anything else it would be a disaster."
Argentina coach Daniel Orsanic added: "The guys were amazing today. Juan Martin won an incredible match and Federico played the match of his life."
Delbonis was beaten by Cilic in five sets in Friday's first singles match but blew away the 37-year-old Karlovic, an opponent ranked 21 places above him, in just over two hours.
The world number 41 broke Karlovic -- the oldest player to feature in a Davis Cup singles match since 43-year-old Australian Norman Brookes in 1920 -- four times to help Argentina banish the memories of losing finals appearances in 1981, 2006, 2008 and 2011.
But much of the credit will go to Del Potro after the Olympic silver medallist, who missed the majority of 2014 and 2015 through injury, outlasted Cilic in an epic five-hour battle of former US Open champions.
"I was positive all the time and did not let my head drop after going two sets down," said Del Potro.
"This was an emotionally exhausting match and one of the biggest wins of my career.