Mexico, the CONCACAF champion and one of the tournament favorites, missed several good chances hitting the post twice, including with a free kick from Jorge Espericueta in the final minute.
Having lost 2-1 to Greece in its previous game, Mexico finds itself at the bottom of Group D with a match against Mali remaining. Paraguay has four points, while Greece and Mali played later Tuesday.
In Group C, El Salvador improved its chances of advancing with a victory that put its first points on the board.
Australia, which had earned a deserved 1-1 draw against Colombia, started well with Joshua Brillante putting the young Socceroos ahead in the ninth minute.
But El Salvador, which lost 3-0 to Turkey in its opener, tied it just eight minutes later. Jairo Henriquez delivered a deep cross which Kevin Barahona headed back across goal and into the path of Diego Coca, who scored.
Jose Pena provided the winner in the 40th, steering home a low cross from Miguel Ochoa.
The other Group C match features home side Turkey against Colombia later Tuesday. A victory for the Turks would send them into the round of 16 alongside Spain, which qualified Monday.