Venezuela's stunning 2-1 victory over fancied Chile was the only one of the quarter-finals not to go to extra-time, while two ended in penalty shootouts, Brazil losing 2-0 to Paraguay after Argentina went out against old rivals Uruguay on Saturday.
"It's a historic achievement but our players aren't satisfied with that, they want more, above all because we said we would beat Chile," Venezuela coach Cesar Farias told reporters.
"I'm surprised that after every match that Venezuela have played, every team that we've played against has said that we've played poorly or that we don't deserve anything. Well, that's fine. Let them continue to look down on us."
The semi-finals were left devoid of South America's big two, Brazil and Argentina, who had meet in the two previous finals both won by the Brazilians, and also Colombia, who had emerged as title contenders until they were upset by Peru on Saturday.
The semi-final line-up has Uruguay, on course for a record 15th title, facing Peru in La Plata on Tuesday and Paraguay against Venezuela in Mendoza.
Peru have been one of the weaker teams in the region for decades, while Venezuela had never been this far before.
Brazil, who drew 2-2 with Paraguay in the group phase, dominated their quarter-final in La Plata from start to finish.
But the Brazilians, who scored six goals altogether, failed to put away their many chances while Paraguay clung on with dogged defence and a brilliant performance from goalkeeper and captain Justo Villar.
"We worked hard, we were far superior [to Paraguay] and we didn't score a goal which is the most important part of football," Brazil coach Mano Menezes told the post-match news conference.
MISSED PENALTIES
Brazil fluffed their lines badly in the shootout with three penalty misses and one saved by Villar, while Paraguay did enough converting two of the three they needed to take to go through.
"Brazil should have won, probably in the 90 minutes," Paraguay's Argentine coach Gerardo Martino said. "We managed to clear two balls off the line and our goalkeeper other [chances].
"We played a totally different match from what we would have liked... it would be great to be able to say we planned it like that but all we can say today is there was a lot of sacrifice, heart, a good percentage from the goalkeeper and lots of luck."
Neymar and Alexandre Pato, who scored two apiece in the 4-2 win over Ecuador, missed chances and Villar saved from defenders Maicon and Lucio and playmaker Paulo Henrique Ganso.
Brazil's Lucas Leiva and Antolin Alcaraz of Paraguay were sent off for fighting near the end of extra-time.
In San Juan, where Chile enjoyed virtual home advantage just across the Andean border from home, centre-back Oswaldo Vizcarrondo put Venezuela ahead with a header from a Juan Arango free-kick and Humberto Suazo equalised with 20 minutes left.
Venezuela's left-back Gabriel Cichero scored the winning goal nine minutes from time, stabbing home after keeper Claudio Bravo parried another Arango free-kick.
"If we divide all the matches we have played into halves, we only played one one badly, today's first half. All the rest was positive," Chile's Argentine coach Claudio Borghi said.
