Replacement Paulo Canavosio was the Azzurri's hero as he crossed for the game's only try with the last move of the game to bring his side to within a point of their hosts in Cordoba.
That left full back Andrea Marcato with the task of firing home the tricky conversion to notch Italy's first win over the Pumas since 2005. He hit the mark and the southern hemisphere had notched their second win in 10 fixtures this summer against their northern counterparts.
It was only the fifth time in 15 meetings that Italy had beaten Argentina and the defeat will send the Pumas back to the drawing board. They drew their two match series with the Scots 1-1 prior to this game.
The Pumas were six points to the good in as many minutes thanks to two penalties from Juan-martin Hernandez, but the mercurial Stade Francais Paris outside half was forced to retire after only 20 minutes with a wrist injury.
That meant Marcelo Bosch had to take over the kicking duties and he kicked two penalties of his own to guide the third ranked team in the world into a handy 12 point lead.
But Marcato's boot gradually brought the visitors back into contention and he had the final word with his last gasp conversion to clinch a famous victory.
This victory came a week after a makeshift Italian side were beaten in Cape Town by the Springboks.