It was Alexis Sanchez’s audacious chip from 12 yards that proved to be the winner in Santiago after Matias Fernandez, Arturo Vidal and Charles Aranguiz had all found the target with powerful efforts.
Lionel Messi scored the first penalty for Argentina but Gonzalo Higuain blazed over the bar and Ever Banega’s weak spot-kick was saved to leave Argentina without a Copa America title since 1993.
There was a lively start to the game with both teams trying to push high up the pitch and Angel di Maria had the first chance of note as he fired over the bar.
The first genuine chance fell to the hosts, though, and Argentina had to be grateful to goalkeeper Sergio Romero.
Sanchez’s cross was only half-cleared by Martin Demichelis and Vidal was on hand to hit a crisp volley which Romero did well to deal with.
The next major chance came down the other end and this time it was Chile stopper Claudio Bravo who was called upon to get his team out of trouble.
Jean Beausejour’s foul on Pablo Zabaleta allowed Messi to whip a ball in to the near post and Bravo did brilliantly to save Sergio Aguero’s point-blank header.
Di Maria had been the subject of some robust treatment by Chile and left the field with what looked like a hamstring injury just before the half-hour, with Ezequiel Lavezzi coming on.
Francisco Silva had earlier been booked for a tug on Di Maria and Gary Medel became the second Chilean to go in the book after a clumsy raised boot to the midriff of Messi.
Both sides then had chances as half-time approached, with Sanchez bringing a save from Romero and Lavezzi firing straight at Bravo.
Marcelo Diaz was booked just before half-time and, while the second half was not as frenetic, it was no less competitive with Marcos Rojo and Javier Mascherano both going in the book in quick succession.
Argentina were having the better of it, with Chile not seeing as much of the ball, but chances were at a premium with Messi firing a free-kick into the wall.
Despite the Albiceleste dominating possession, it was Chile who created the best chance of the half, Sanchez’s cross finding Vidal at the back post but his shot was blocked.
La Roja looked to have weathered the storm and began to gain more possession but both sides were struggling to create clear-cut chances and the game headed into the final 10 minutes with extra-time looming.
Sanchez then did have a chance as he latched onto a ball over the top but could only volley wide and in the final minute of stoppage-time Argentina had a golden chance to snatch it.
Messi freed Lavezzi in the box and he chose to cross to Higuain when he maybe should have shot and the striker could only find the side-netting.
With all previous knockout games in the tournament going straight to penalties, the 2015 Copa America had its first spell of extra-time and it was Chile who had the more possession with Diaz firing over the bar.
Sanchez then blazed over after bearing down on goal from around halfway the deadlock could not be broken and the game went to penalties.