Paraguay took the initiative from the kick-off and Greece goalkeeper Alexandros Tzorvas made a good early save with his legs from Lucas Barrios.
The Greek defence was in total disarray and Paraguay took the lead in the ninth minute, Enrique Vera tapping gleefully home after Roque Santa Cruz's shot came back off the post.
Paraguay continued to dominate and Barrios made it 2-0 in the 25th minute after Santa Cruz's header was well saved.
Otto Rehhagel's Greece team, who looked one-paced when they were held to a 2-2 draw by World Cup finalists North Korea last week, struggled again and their play was characterised by wayward passing, poor movement and a lack of creativity.
Greece did put the ball in the net with their first shot on target in the 33rd minute but Dimitris Salpingidis's tap-in from a Sotiris Ninis cross was correctly ruled out for offside.
The 2004 European champions begin their World Cup campaign against South Korea on June 12 in Group B which also includes Argentina and Nigeria.
Paraguay face reigning champions Italy, New Zealand and Slovakia in Group F.
