Mexico finished a point ahead of El Salvador, which entered the match already advanced to the quarterfinals and needing only a tie to win the group.
By finishing first, Mexico avoided a possible match against the U.S. until the final.
The quarterfinal matches for Mexico and El Salvador are Saturday in Glendale, Arizona.
Meanwhile, El Salvador, coached by former U.S. men's national team player Hugo Perez, recorded consecutive 2-0 wins vs. Trinidad and Tobago and Guatemala.
Mexico got the goal it needed on Sunday when Hector Herrera found a seam in the defense and exploited it with a diagonal ball to Rodriguez on the right flank.
Rodriguez used his first touch to push the ball to the middle of the field at the top of the penalty area. A second touch put the ball on his left foot in position for a shot that deflected off El Salvadoran defender Ronald Gomez, leaving no chance for Mario Gonzalez to make the save.
Gonzalez kept El Salvador alive with a save on Rogelio Funes Mori early in the second half.
Mexican goalkeeper Alfredo Talavera had nothing to do until the 62nd minute when a turnover created an opportunity for Joaquin Rivas. Talavera used his right hand to make the save, and the rebound attempt by Joshua Perez was blocked by Hector Moreno.
El Salvador nearly equalized in the 71st minute on a free kick by Alexander Larin that hit the left post.
Gonzalez then denied Orbelin Pineda with a parry of his strike from distance in the 74th minute. Gonzalez had five saves.