Paraguay defender Dario Veron scored the winning spot-kick, blasting the ball past Renny Vega, to send his side into Sunday's final against Uruguay in Buenos Aires, but celebrations were marred by an ugly fight that broke out amongst the teams as they left the field.
The result was harsh on Venezuela, who will feel desperately unlucky they did not win the match before the shootout. They hit the woodwork three times and dominated the later stages against Paraguay, who had midfielder Jonathan Santana sent off in the first period of extra-time.
The Paraguayans then took advantage of their good fortune to convert all five of their penalties in the shootout with their goalkeeper Justo Villar saving Franklin Lucena's weak effort to set up the win.
"We've had some luck in these past few days and we had it again today. Clearly we have to improve," Villar told reporters afterwards.
"We've got five or six injured players, another player suspended and we can't go into the final and do the same as we've done in the last few days. Playing for another goalless draw and waiting for the penalties would be too much."
POST-MATCH FIGHT
The post-match fight, involving players and coaching staff from both teams, lasted for several minutes and could lead to further suspensions for Paraguay.
Police then had to escort the players and coaches from the field to protect them from objects thrown from the crowd.
The result meant that Paraguay reached the final of South America's most prestigious tournament without winning a single match in open play having drawn three group matches before beating Brazil on penalties after a goalless draw.
It also brought a halt to Venezuela's remarkable Copa America. Long regarded as the weakest side on the continent, they had never before reached the semi-finals. They will now face Peru in La Plata on Saturday in the third-place play-off.
"Now the whole world knows that in South America there's another team that's got quality," Venezuela coach Cesar Farias told reporters.
"Maybe we can make up for the prize we'd hoped to win here by qualifying for the World Cup in 2014."
SAVED BY THE WOODWORK
The Paraguayans enjoyed the majority of possession in the first half but it was Venezuela who created the best chances.
Towering defender Oswaldo Vizcarrondo looked to have put Venezuela ahead with a 35th minute header but his effort was ruled out for offside, and then Alejandro Moreno crashed a header against the Paraguayan crossbar just before the break.
Paraguay's best effort also came from a header with Vega palming an effort from Veron to safety.
Neither side created a single clear cut chance in a pedestrian second half so Paraguay coach Gerardo Martino threw on his most prolific striker Roque Santa Cruz in a bid to break the deadlock.
However, Santa Cruz lasted just seven minutes before limping off
