Salomon Rondon tucked away a second-half penalty to send Venezuela into the Copa America quarter-finals on Wednesday with a 1-0 win over Mexico in Group B, a result that also sent Jamaica crashing out of the tournament.

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.

The goal was Venezuelan all-time top scorer Rondon's 42nd for his country.

Mexico were awarded a penalty of their own for a handball in the dying minutes after a video review concluded Miguel Navarro had blocked Jorge Sanchez's shot with his left arm.

However, Venezuela goalkeeper Rafael Romo got down low to parry Orbelin Pineda's 87th minute spot kick.

"Sometimes we were not in possession of the ball, but we never gave up," Venezuela coach Fernando Batista said through an interpreter. "They give it their all ... and that makes me very proud."

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

Mexico play Ecuador in Arizona on Sunday in a match that will decide the other qualifier from the group.

Jamaica are out irrespective of the outcome of their last match against Venezuela in Texas having already lost to Mexico and Ecuador.

Venezuela will win the group with a draw or victory in their final match against Jamaica, potentially avoiding defending champions Argentina in the quarter-final stage.

Romo's penalty save was one of five stops that prevented Mexico from finding an equaliser, with his last two saves coming after Pineda's penalty miss.

He first kept out Cesar Huerta's low drive in the 88th minute, then bravely blocked Guillermo Martinez's close-range effort in stoppage time.

"If you generate opportunities as we did, if the man of the match is the opponent's goalkeeper, yes, things weren't as we expected," said Mexico coach Jaime Lozano.

"But there are 90 minutes ahead. No one is getting off this ship. And we will make it."

ANOTHER CAPTAIN DOWN

Mexico dominated the opening half hour but Romo was equal to Santiago Gimenez's weak shot from Luis Chavez's through ball.

Venezuela grew into the game, with Rondon hitting the post with a dipping half-volley in the 34th minute and Yeferson Soteldo forcing Gonzalez into a near-post save in the 50th.

Mexico also lost their captain for the second time in as many group games. Defender Cesar Montes, standing in as skipper for Edson Alvarez, was removed at halftime with an apparent groin injury.

"I saw that he was with a level of discomfort in his groin, and at halftime they told us it was going to be complicated for him to play the second half," Lozano said of Montes.

"So tomorrow or maybe in a couple days we'll have an answer, but today we cannot say if we're going to have him for the next match."

Alvarez's tournament was ended by injury within the first half hour of Mexico's opening win over Jamaica on Saturday.