Argentina, helped by a brace from Juan Roman Riquelme, beat Colombia 4-2 to reach the Copa America quarter-finals on Monday and Paraguay joined with a 3-1 win over United States.
Both teams have six points from two games in Group C and the impressive tally of eight goals apiece.
The US and Colombia are both without points and depend on a complex combination of results to have any chance of qualifying.
The tournament produced yet another refereeing row as Colombia, who scored first, were furious with the penalty from which Argentina equalised.
The ticketing chaos continued as thousands of fans queued in vain in Merida, where hosts Venezuela play Uruguay on Tuesday.
Some said they had paid in advance for their tickets but had not received them.
A Reuters reporter saw touts freely selling black market tickets at up to twice their face value.
Fans accused the government of President Hugo Chavez of buying-up tickets and filling stadiums with their supporters to avert possible protests and anti-government chanting during games.
The government has denied the allegations.
Argentina's match in Maracaibo ended amid chants of "the government's going to fall" and "freedom" echoing around the 42,000-seat stadium.
COLOMBIA FIGHTBACK
On the field, Colombia, beaten 5-0 by Paraguay in their opener, took a shock 10th minute lead with a crafty Edixon Perea backheel.
Argentina levelled 10 minutes later when Lionel Messi went down in what appeared to be a simple 50-50 challenge, but the referee gave a penalty and Hernan Crespo converted.
Crespo, who took his tally to three goals in two games, pulled up as he kicked the ball and was substituted by Diego Milito.
Afterwards, the 31-year-old said he is unlikely to play in the tournament again.
Riquelme then sprang into action, scoring from a nonchalant header and a trademark free kick 11 minutes before halftime.
Although Jaime Castrillon pulled one back for Colombia, Milito ended their fightback with a fourth Argentine goal in stoppage time.
"I think we clearly dominated the win and we deserved our win," said Riquelme.
Colombia midfielder Fabian Vargas, sent off in injury-time, said: "There was no reason for the referee to give a penalty and it made Argentina's life easier."
Earlier, Edgar Barreto gave Paraguay a 30th minute lead in Barinas before Ricardo Clark scored from the edge of the area to make it 1-1 at halftime.
Second-half goals from Oscar Cardozo and Salvador Cabanas, who took his tally to three despite making only two second-half substitute appearances, won the game for Paraguay.
The US created plenty of chances and substitute goalkeeper Aldo Bobadilla, who replaced the injured Justo Villar in the second half, made three important saves to keep Paraguay ahead.
Colombia and the US still have an outside chance, with the two best third-placed teams in the three groups also qualifying for the last eight.