It was a comfortable victory over the course of 90 minutes for last year's World Cup runners-up, who will now meet hosts Chile in Saturday's final, but it could have been a much tougher night had Paraguay taken an early chance when Roque Santa Cruz volleyed wide after being found by Nelson Valdez.
The deadlock was broken a few minutes later when Lionel Messi's free kick caused problems for the Paraguayan defence, whose failure to clear the danger allowed Marcos Rojo to fire home from close range.
Pastore made no mistake with his next opportunity as Messi once again found the space to pick out the PSG attacker, and his low strike left Villar helpless as Paraguay's defence was breached once again.
However, the lead was no longer comfortable a minute before the interval as a hopeful ball forward sliced open the Argentina back four and played in Lucas Barrios, who kept his composure to beat Sergio Romero.
Any hopes of a fightback from Paraguay were ended when Argentina scored twice in the space of six minutes in the early stages of the second half, with Angel di Maria proving to be the difference.
The Manchester United winger first made it 3-1 by collecting a pass from Pastore before taking the ball past Bruno Valdez to fire home, and he scored his second of the night from close range after Pastore's effort was kept out by Villar.
Messi continued to influence the game throughout the second half and his pass for Di Maria almost resulted in another goal when a cross just evaded Sergio Aguero in the box.
Paraguay struggled to pose a threat at the other end after falling further behind, and Argentina added a fifth when Aguero drifted into space to head home an inviting ball from Di Maria.
There was still time for Gerardo Martino's side to pile further misery on Paraguay in the closing stages as Messi registered a third assist by finding Gonzalo Higuain, who finished emphatically just a few moments after coming on.