Rondon made no mistake from the spot in the 57th minute after Jon Aramburu was brought down inside the box by Julian Quinones, sending Mexico keeper Julio Gonzalez the wrong way and slotting home into the bottom corner.

Mexico earned a penalty of its own for a handball in the dying minutes, but Rafael Romo got down low to save Orbelin Pineda's 87th minute spot-kick.

The win moved Venezuela, which beat Ecuador in its opening match, up to six points at the top of the group and secured its progress to the last eight with a game to spare.

Mexico plays Ecuador in Arizona to close out its group fixtures in a match that will decide the other qualifier from the group.

Jamaica, though, is out irrespective of the outcome of its last match against Venezuela in Texas, having already lost to Mexico and Ecuador.