Having finished 0-0 in regulation and then extra time, both sides were forced to determine a winner in an evenly-fought contest from the spot in Santiago.
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All eyes were on Alexis Sanchez as he approached the spot with a chance to make history for the host nation, and he made no mistake by converting the penalty that ends La Roja's 99-year wait in the Copa.
Eduardo Vargas had the first opening of the game when he was afforded space and time to line up a strike outside the box and he drilled his effort inches past the post.
Chile maintained the pressure and Sanchez raided down the right flank and whipped a low cross into the box which was poorly cleared away by Martin Demichelis. Arturo Vidal picked up the loose ball and fired a volley towards the bottom corner, but Sergio Romero got down well to make the stop.
Argentina had their first opening at goal from a free kick from the right as Lionel Messi whipped in a cross to find Sergio Aguero at the near post, but the striker's effort was comfortably saved by Claudio Bravo.
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La Roja had an excellent chance to take the lead when Vargas broke away up the middle of the pitch and coasted past the last defender, only to lose his composure at the vital moment by firing his shot over the bar.
Argentina could have opened the scoring just before the break when Javier Pastore found space down the right and picked out substitute Ezequiel Lavezzi in the middle, but he could only fire his strike straight at Bravo.
In the second half, Sanchez robbed Otamendi of possession on the edge of the box, but was forced wide by the defender. The Arsenal man lifted a cross to the back post for Vidal, although he could only direct his header straight at Romero.
The 27-year-old probed again for La Roja as he tried to weave his way past Otamendi, and he managed to guide the ball to Vidal on the edge of the box, but his effort was well blocked by Pablo Zabaleta.
Sanchez almost unlocked the Argentina defence when he latched on to a cross into the box and fired a volley towards the bottom corner, but his strike went agonisingly wide of the post.
La Albiceleste had a great opportunity to win the game in the dying seconds of normal time as Messi released the run of Lavezzi down the flank, but the winger opted to fire the ball across the face of goal rather than shoot. As a result, Higuain could not turned the ball home at the back post as he fired his strike into the side-netting.
Jorge Sampaoli's men had the only clear chance in extra time as a rare error from Javier Mascherano saw Sanchez race through on goal, but he failed to keep his effort below the bar as penalties loomed.
Successful conversions from Matias Fernandez, Messi and Vidal saw Chile lead 2-1, but the home fans dared to dream when Higuain blazed over the bar.
Goals from Charles Aranguiz and Sanchez, either side of Banega's miss, was enough as Sampaoli's men clinched the title on home soil to sweeten the deal.