"We were convincing at all the right moments," goalkeeper Guillermo Ochoa told reporters after the game.
The Uruguayans, who won their 15th title in Argentina in 2011, pushed Venezuela back in the second half but lacked poise in front of goal and Muslera prevented them going further behind with a fine save from Adalberto Penaranda in the 68th minute.
Edinson Cavani came close to equalising in the dying moments but was wide with one chance and had another saved by Dani Hernandez.
"Luckily I had time to get there and finish." The victory marked the first time Venezuela have notched two consecutive Copa America wins, while Rondon became the first Uruguay player to score in three Copa America tournaments. The majority of my players did not have a good game," disappointed Uruguay coach Oscar Tabarez told local radio.
"The Uruguay that we are saw today are a long way from the Uruguay we saw play not that long ago." Venezuela and Mexico, who each have six points in Group C, will meet next week to decide who will win the group, while Jamaica were also eliminated with Uruguay, the most successful Copa America nation.
Venezuela pulled off the shock of the Copa America so far by stunning Uruguay 1-0 to reach the quarter-finals, while Mexico also advanced with a 2-0 win over Jamaica.
Midfielder Alejandro 'Lobo' Guerra lobbed Fernando Muslera from more than 30 metres and although the Uruguayan goalkeeper got a finger tip to the ball, it bounced off the bar and fell to Rondon who tapped it into the net."It was incredible what 'Lobo' did, the wit he had to hit it," Rondon said.There was to be no upset in the other match, however, with Mexico taking the lead after 17 minutes in Pasadena through Javier 'Chicharito' Hernandez.The diminutive striker rose unmarked to pinpoint a glancing header into the bottom corner of the net after Jesus Corona had crossed from the left.Mexico were the better side, however, and Oribe Peralta, who came on for Hernandez after 77 minutes, scored just three minutes later after a quick break.
The win was coach Juan Carlos Osorio's 10th consecutive victory since taking over last year.