Talisman Lionel Messi, who is still searching for his first international title, set up Lautaro Martinez for the opener in Brasilia after seven minutes, but Luis Diaz found a second-half equaliser for the Colombians, which sent the game to penalties.
While Messi converted from 12 yards, Aston Villa keeper Emiliano Martinez proved to be the hero, saving from Davinson Sanchez, Yerry Mina and Edwin Cardona to give Argentina a 3-2 victory on spot-kicks.
Lionel Scaloni’s side will now aim to end a 28-year trophy draught, while the hosts are hoping to repeat their triumph of two years ago, when they overcame Peru 3-1 in the final.