Canada goalkeeper Sabrina D'Angelo tipped Betina Soriano's shot onto the crossbar in the opening seconds of the match, but a sixth-minute dismissal of Argentina's Agustina Barroso for knocking over Christine Exeter led to Shelina Zadorsky's penalty a minute later.
Jaclyn Sawicki added another goal in the 20th minute before Leon - with the help of a pair of assists from Sawicki - tacked on goals in the 22nd, 42nd and first minute of first half injury time.
It was the third time a Canadian had scored three or more goals in at the U-20 Women's World Cup following Christine Sinclair (2002) and Brittany Timko (2004).
Catherine Charron-Delage completed Canada's domination in the 86th, heading in Jade Kovacevic's cross.
The win was the third time Canada had scored six goals or more in a game at the U-20 Women's World Cup, and first since 7-0 victory over Thailand in 2004.
Canada will face Norway on Thursday before finishing its Group C schedule against North Korea.