Alexis Sanchez scored the game-winning penalty for Chile after Gonzalo Higuain blasted his attempt way over the crossbar and Ever Banega's shot was saved by Claudio Bravo.
While Chile celebrated winning in front of their home fans at the Estadio Nacional Julio Martinez Pradanos in Santiago, Lionel Messi, who was the only Argentina player to find the back of the net with his penalty attempt, and the rest of his team-mates could only look on in utter dejection and imagine what could have been.
Not only does Argentina's 22-year wait for a major trophy go on, but this is the second heartbreak they have endured in a final after losing to Germany in extra time in the 2014 World Cup.
Eduardo Vargas almost gave Chile the lead in the in the 10th minute when his scorching shot from 25 yards flashed just wide of the post.
Arturo Vidal nearly put Chile ahead just one minute later when Sanchez's shot was deflected to him by Martin Demichelis. However, Vidal's volley was superbly saved from going in to the bottom corner by Argentina goalkeeper Sergio Romero.
Argentina were presented their first chance to score in the 20th minute, but Sergio Aguero could not put Messi's pass past Bravo.
Sanchez and Argentina winger Ezequiel Lavezzi, who came on as a substitute for Angel Di Maria after he picked up a hamstring injury, both had opportunities to put their respective teams ahead right before the end of the first half, but failed to do so.
Sanchez had a chance to redeem himself in the 82nd minute, but his sweetly struck volley went just inches wide of the post.
Argentina could have walked away with the Copa America title in the dying seconds of the game when Higuain could not take advantage of Lavezzi's pass and fired it into the side netting.
Sanchez had the only opportunity to score in the first half of added extra time as the Arsenal winger pounced on Javier Mascherano's mistake before his shot went over the crossbar.
Lavezzi appealed for a penalty with five minutes remaining in added extra time, but the referee waved him away and the match ultimately headed to penalties.
Matias Fernandez and Messi scored for Chile and Argentina respectively before the tournament hosts dominated the rest of the shootout as Higuain skied his attempt over the bar and Bravo saved Banega's poor attempt. With a 3-1 lead in hand, Sanchez coolly slotted the ball past Romero to lead Chile to Copa America glory.