Claudio Bravo made the decisive save in the shoot-out as Francisco Silva converted the winning penalty in New Jersey.
Both Argentina and Chile were reduced to 10 men in a fiery first half in a rematch of last year's decider, as Marcos Rojo and Marcelo Diaz saw red, and neither team could break the deadlock after 120 minutes of play in front of more than 82,000 fans at MetLife Stadium.
And for the second successive year, a shootout was required to determine a winner, with Chile coming out on top again following spot-kicks as Argentina's 23-year wait for a major trophy continued.
After captain and goalkeeper Claudio Bravo denied Sergio Aguero with a stunning finger-tip save in extra time, he was at it again in the shootout, keeping out Lucas Biglia's effort following Lionel Messi's skied shot over the bar as Francisco Silva stepped up and converted the winning penalty.
The 4-2 shoot-out loss marked a third consecutive defeat in a final for Argentina, beaten last year as well as the 2014 World Cup.
Despite concerns about Angel Di Maria's fitness, the star attacker returned to the starting lineup in place of the injured Ezequiel Lavezzi. Biglia also replaced Augusto Fernandez in midfield following the 4-0 rout of the United States.
Chile also made two changes after their 2-0 win over Colombia, with Arturo Vidal back in the XI having served a one-game suspension. There was also room for Diaz as Silva and Pablo Hernandez made way.
While Ever Banega had a chance inside the first minute, trying his luck from distance with Bravo left scrambling across his line as the ball flashed just wide of the post, the early exchanges were typical of South American football with more fouls and less action.
Despite the stop-start nature of the match, Argentina did settle quickest and loomed as a constant threat in attack and they should have been ahead in the 21st minute.
In a similar scene to the 2014 World Cup final, which Argentina lost to Germany in extra time after Gonzalo Higuain wasted a gilt-edged opportunity in the first half, the in-form Napoli striker bottled another golden chance on the big stage, pouncing on Gary Medel's slip and charging through on goal only to see his chip over Bravo drift agonisingly wide of the woodwork.
And just as Chile was left counting their blessings, things quickly turned sour for the title holders when Diaz was sent off by referee Heber Lopes approaching the half-hour mark for a second bookable offense, having blocked Messi.
With tensions simmering however, Argentina's numerical advantage was short-lived after Rojo was shown a straight red card in the 43rd minute for a tackle from behind on Vidal, sparking a melee.
The second half was somewhat subdued compared to the first, as the match opened up, but neither team really tested the opposing keepers.
Not even the introduction of Aguero, in place of Higuain, could spark Argentina as fans watched on in silence, such was the lack of action in the respective attacking thirds, though Chile star Eduardo Vargas did force Sergio Romero into a low diving save with 10 minutes remaining.
Messi engineered an opening for Aguero in the 85th minute but the Manchester City forward wasted a good chance, unable to keep his effort under the crossbar.
There was action in the remaining seconds when Jean Beausejour sprinted forward and picked out Alexis Sanchez inside the six-yard box, though he was denied by Ramiro Funes Mori's last-ditch tackle, while Messi fired a powerful shot wide of the post at the other end as the match headed to extra time.
The game came to life in the additional period, with Bravo producing one of the saves of the tournament to tip Aguero's goal-bound header over the bar and keep the scores level in the 101st minute, after Romero dealt with Vargas and his effort just moments earlier.
Both Vidal and Messi missed the opening penalties, but Chile emerged triumphant thanks to Nicolas Castillo, Charles Aranguiz, Beausejour and Silva, as Bravo's save paved the way for victory.