La Legion were 2-1 down heading into the final two singles matches on Sunday, but Juan Martin del Potro set the tone by battling back from two sets down to beat Marin Cilic, a result that levelled the final up at 2-2.
Federico Delbonis then secured a straight sets victory over Ivo Karlovic to hand Argentina their first-ever Davis Cup and Orsanic had nothing but praise for his team after the victory was assured, particularly Del Potro, who has overcame a number of injury problems in recent years.
Orsanic said: "It is a great honour to be a team captain to this group of professionals. What Del Potro did was amazing, his achievement borders the impossible."
Del Potro, who broke his finger during the fifth set of his clash with Cilic, was alsodelighted by Argentina's success, while admitting that he never lost faith that they could secure overall glory.
The 2009 US Open champions said: "My finger is broken but I won't mind one bit. It happened in the fifth set when I tried to catch a serve from Cilic which was out."
"I was positive all the time, I didn't let my head drop after going down two sets."