Victor Ayala was brilliant for the victors, setting up the first and third goals for Paraguay, as they leapfrogged Bolivia into eighth on the CONMEBOL table and moved within five points of fifth.
Paraguay hit the front in just the 16th minute on Friday when Ayala got free on the right wing and whipped a cross towards the six-yard box.
Bolivia's goalkeeper Sergio Galarza, who had a terrible game, missed the cross as he dived to push it away, which allowed Paraguayan attacking midfielder Jonathan Fabbro to take a touch before side-footing the ball into the net.
Ayala and Fabbro both almost doubled Paraguay's lead just before the half-hour mark with the former bursting through Bolivia's defence before Galarza saved at his feet, while Fabbro's shot on the rebound was headed off the line by the visitors' captain Ronald Raldes.
Fabbro continued his fine first period when his 30-yard strike was tipped over the bar by Galarza just before the break but Paraguay finally doubled their lead two minutes after half-time.
Miguel Samudio's wicked left-wing cross picked out Roque Santa Cruz in the penalty area and the Paraguayan captain looped his header perfectly over Galarza and into the top corner of the net.
Bolivia seemed more positive in the second half and just before the hour mark Marcelo Martins unleashed a bicycle kick, which Antony Silva was able to hold onto in Paraguay's goal.
Ayala continued to be Paraguay's best outlet for goal-scoring opportunities with the 25-year-old right winger setting up Arnaldo Sanabria in the 70th minute but the substitute volleyed wide at the near post.
But Paraguay made their dominance count 10 minutes later when Richard Ortiz played a one-two with Santa Cruz to carve open Bolivia's defence and the former scored.
It was 4-0 in the 84th minute as Galarza flapped at another fine corner from Ayala and Paraguayan defender Gustavo Gomez headed home at the back post.
The victory means Paraguay are still well in the hunt for fifth position in South America, which carries with it a spot in a two-legged play-off versus the Asian Football Confederation's fifth-placed team for a berth at next year's World Cup finals.
With four games remaining in CONMEBOL's World Cup qualifying, Paraguay have 11 points, while fifth-placed Uruguay have 16.
Venezuela sit behind Uruguay on goal difference in sixth, while Peru are seventh on 14 points.
