Emiliano Martinez was the hero of this shootout and saved three penalties, with the game ending at 1-1 after extra time.
Argentina led the way when Lionel Messi bid to win his first major international competition. Lautaro Martinez scored from within the Colombia box.
Colombia won the match just after the hour mark, when Luis Diaz grabbed a quick-taken free kick to lift a shot past Martinez.
After both teams had opportunities in the first half, Wilmar Barrios hit the post for Colombia and Yerry mina hit the bar from a corner. Nicolas Gonzalez was denied by David Ospina at one end.
Argentina had a golden opportunity to score a winner in the second period. Angel Di Maria round Ospina set up Martinez but Barrios was able to block the striker’s shot.
Juan Cuadrado, Messi and Rodrigo De Paul scored the first penalties in the shootout.
Martinez made it a point to speak to the Colombian players before they took their spot kicks. Mina was then saved by Martinez.
Martinez was the goal scorer for Argentina, scoring the third spot from the spot. Martinez then made his third save in the shootout to deny Edwin Cardona's side and give them victory.
"The truth is that I don't know the words," stated Martinez.
"We were kept in quarantine for 40 days. We were the only national team without access to anyone. We were in our bubble all by ourselves, along with the cleaners, cooks, and directors.
"It's the dream of 70 people. We have said it from the beginning: we want to play in the final. What could be better than playing Brazil on their pitch?
Brazil will face Argentina in Rio de Janeiro's Maracana Stadium this weekend, in an attempt to win the Copa America title. Brazil beat Peru earlier in this week's semifinals. Brazil is now aiming for its sixth Copa America title.