Argentina went ahead early through goals from Marcos Rojo and Javier Pastore, with Lucas Barrios Caceres grabbing one back for Paraguay before the break.
The second half was all Argentina though, with Angel Di Maria grabbing a brace before Sergio Aguero and Gonzalo Higuaín added their names to the scoresheet.
Argentina only had to wait 15 minutes to open the scoring and it came after Paraguay failed to clear Lionel Messi's free-kick, with Rojo pouncing on the loose ball and slotting it past goalkeeper Justo Villar.
Gerardo Martino's side had a golden opportunity to make it 2-0 just six minutes later, but Pastore aimed his shot straight at Villar.
Pastore atoned for his mistake in the 27th minute when he latched on to Messi's superb pass and drilled it into the bottom corner.
Paraguay brought themselves back into contention on the stroke of half-time as Pedro Benitez headed a dangerous balll to Barrios after a poor clearance from Argentina, who the striker proceeding to fire past Sergio Romero.
While Paraguay would have been thinking about causing an upset after having reduced the deficit, Argentina all but ended their hopes of a comeback with a third goal in the 47th minute when Di Maria slotted Pastore's through ball across Villar and into the corner of the net.
Di Maria grabbed his second goal just five minutes later when he side-footed home a rebound after Villar saved a Pastore's toe-poke following some strong running from Messi engineered the opportunity,
Manchester City striker Sergio Aguero made it 5-0 in the 80th minute when he snuck in between two defenders to head past Villar after Di Maria had whipped the ball in.
Argentina completed the riot three minutes later when Higuain's shot from close range flew into the roof of the net after he was brilliantly set up by the fleet-footed Messi.
Geraldo Martino's side now face Chile in Saturday's finale, while Paraguay will face Peru in the third/fourth play-off on Friday.