Paredes, who went on as a second-half substitute, chipped in after a corner in the 67th, and Vidal soared high and angled in a header in the 73rd - again from a corner.
Fielding a youth team, Mexico took an unlikely lead in the 41st via Nestor Araujo's header after Chile had dominated possession.
Chile was just as dominant in the second half - probably the best team so far in the tournament - but this time converted after key forwards Humbeto Suazo and Alexis Sanchez were thwarted in the first half.
Suazo had a chance early in the half before Chile finally broke through, hitting Luis Ernesto Michel in the face with a close-range shot which the Mexico keeper somehow smothered in the 53rd minute.
Despite Chile's dominance, Mexico had two chances to equalize in the final seconds with Chile keeper Claudio Bravo coming up with a key save on Edgar Pacheco.
It was an important victory for new Chile coach Claudio Borghi, who took over when Marcelo Bielsa resigned after leading Chile to its best World Cup performance since 1962.
Because it plays in the CONCACAF region, Mexico is playing in the South America championship as a guest and with a young team. Stars like Javier Hernandez, who led Mexico to the Gold Cup title last month against the United States, were not selected.
Mexico was further weakened when eight players were kicked off the team for violating training rules after a friendly match in Ecuador.
Chile: Claudio Bravo, Pablo Contreras, Waldo Ponce, Gonzalo Jara, Mauricio Isla, Gary Medel, Arturo Vidal, Matias Fernandez (Carlos Carmona, 83), Jean Beausejour (Esteban Paredes, 60), Alexis Sanchez, Humberto Suazo (Marco Estrada, 92).
Mexico: Luis Ernesto Michel, Hector Reynoso, Darvin Chavez, Hiram Mier, Javier Aquino (Oribe Peralta, 74), Paul Aguilar, Diego Reyes, Nestor Araujo, Jorge Enriquez, Giovani Dos Santos, Rafael Marquez Lugo (Edgar Pacheco, 88).