Paraguay had the first real chance after four minutes from an indirect free kick in the area, but Jorge Rojas could only blast his effort over the crossbar, much to the relief of Jose Abella, who had made the error.
Armando Zamorano came close to handing Mexico the lead with 20 minutes on the clock, but the 19-year-old's effort just moved past the post at the vital moment.
Marco Bueno was next to come close for Mexico in the latter stages of the first half, but the attacker could only roll his effort wide of the post as the two sides entered the interval level.
Arnaldo Sanabria had the ball in the back of the net for Paraguay in the early stages of the second half, only for the referee to spot a foul in the build-up.
However, they had their lead moments later when Derlis Gonzalez burst into the box before clipping a fine effort into the top corner.
Both sides had chances as the match became stretched in the latter stages, but it was Paraguay who held on for the vital three points.
Next up for Mexico is a clash with Mali on June 28, while Paraguay face Greece on the same evening.