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.
"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.
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.
