A victory for Filippo Volandri's Italy will earn them only their second Davis Cup crown in the elite men's team competition after their triumph in 1976.
Lleyton Hewitt's Australia are looking to capture their 29th title and close the gap on the United States, who are at the top of the all-time list with 32 trophies.
Arnaldi traded breaks with Popyrin early in a fiercely contested opening set before the world number 44 broke in the 12th game to grab the early advantage in the match.
A more aggressive Popyrin raced 4-0 ahead in the second set and comfortably levelled the match but Arnaldi responded superbly in the decider to secure victory with a decisive break.
World number four Jannik Sinner, whose heroics in singles and doubles helped Italy quell the challenge of Novak Djokovic's Serbia in Saturday's dramatic semi-final, can clinch the tiesagainst Australian number one Alex de Minaur later on Sunday.
Simone Bolelli and Lorenzo Sonego are scheduled to face the experienced Australian pair of Matthew Ebden and Max Purcell if the tie heads to a doubles decider.
