With the teams all square after five attempts each in the shootout, Wilker Angel had his spot-kick saved by Maxime Crepeau and Ismael Kone buried the winning penalty to send Canada through.
"Emotions are running high, I'm so happy for everyone who is supporting us," Crepeau, who made two saves in the shootout, told Fox Sports.
"It's a lot of work and now we have the fruit of our hard work. This is amazing to be in the semi-finals of Copa America. I think everybody needs to realise this country and its footballers deserve respect."
Canada, playing in their first Copa America, will face Argentina in New Jersey on Tuesday for a chance to play in the July 14 final. The semi-final will be a rematch of the tournament's opener, in which the defending champions Argentina claimed a 2-0 win.
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