
The home side pulled ahead early in the game, with a goal from Nelson Haedo Valdez in the 9th minute, and Christian Riveros made things 2-0 in the 26th minute.
Five minutes into the second half Roque Santa Cruz added a third. The game appeared to be all Paraguay's, but Ivan Kaviedes put the score 3-1 to sketch a recovery in the 80th minute.
The host introduced substitutes to preserve key players Haedo Valdez, Santa Cruz and Claudio Morel Rodriguez ahead of Wednesday's clash against Chile. However, it did not allow the rival any delusions and scored a fourth goal two minutes later, through Nestor Ayala.
Riveros added the second in his personal count soon afterwards, to leave the count 5-1.
Paraguay is now on 7 points, to Argentina's perfect record on 9. Brazil - which was set to play away in Peru on Sunday - remains on 4 points, from a draw in Colombia and a home win against Ecuador.
Ecuador - who has played the last two editions of the World Cup - remains the only team to have lost all three games in the South American qualifying round, with 11 goals against and only 1 in favour.