The two Copa America-bound nations played out stingy contests to open their respective 2015 campaigns - the Mexicans accounting for Ecuador 1-0, while Paraguay drew 0-0 with Costa Rica earlier in the international break.
Miguel Herrera's Mexico are the more fancied of the two to progress at the continental tournament.
Herrera said striker Javier Hernandez - who scored the winner against Ecuador - was still an asset for his side, despite him being starved of opportunity on loan at Real Madrid from Manchester United.
"Javier may be frustrated mentally but when he gets on the field, he's ready to go up against anyone," Herrera said after the friendly in Los Angeles.
Herrera does have a selection headache at the other end of the park, after Jesus Corona saved a Miller Bolanos penalty on his way to a clean sheet against the Ecuadorians.
Corona, number two to Guillermo Ochoa, has thrown his hat in the ring to be the primary custodian ahead of the showpiece tournament in Chile.
Paraguay, meanwhile, are in the infancy of a new reign, after Ramon Diaz's bow in their stalemate with Costa Rica.
Diaz's chargers hit the training track on Sunday morning, with 14 of them in action including: Victor Caceres, Roque Santa Cruz, Edgar Benitez, Osvaldo Martinez, Antony Silva, Lucas Barrios, Fidencio Oviedo, Fabian Balbuena, Hernan Perez, Osmar Molinas, Gustavo Gomez, Ivan Piris, Jorge Moreira and Fernando Fernandez.
The full squad was set to train later in the day at Sporting Kansas City's Arrowhead Stadium.
