Marcos Rojo put Argentina ahead from Lionel Messi's free-kick and Javier Pastore made it 2-0 with a low shot.
Lucas Barrios pulled one back from 20 yards, but Angel Di Maria then netted twice, slotting in from Pastore's pass and then converting a rebound.
Sergio Aguero headed in a fifth and Gonzalo Higuain blasted in a sixth.
It was an impressive victory from Gerardo Martino's side as La Albiceleste moved into the Copa America final for the third time in four competitions and will play Chile in Santiago on 4 July.
Although he did not score, it was another influential performance from skipper Messi, who had a hand in three of the six goals.
His free-kick led to Rojo opening the scoring in the 15th minute and then the four-time World Player of the Year created the second with a jinking run before setting up the impressive Pastore.
Paraguay, 85th in the world rankings, had recovered from a two-goal deficit in their group game against Argentina, which ended 2-2.
Barrios, who scored a last-minute equaliser in that match, netted again, just before half-time with a fine effort from 20 yards out.
But there was to be no fightback this time. Early in the second half, Pastore released Di Maria who slid the ball underneath goalkeeper Justo Villar.
Argentina made it four as Messi led a counter attack and set up Pastore, whose shot fell to Di Maria to finish into an open goal.
Di Maria's cross was then headed in by Manchester City striker Aguero before substitute Higuain scored a stunning sixth to complete the rout.
Argentina remain on course to win their first Copa America title since 1993 after thrashing Paraguay to set up a final against tournament hosts Chile.