The 2010 quarter-finalists, who had struggled through the qualifiers under two previous coaches, made it seven goals in two matches after their 3-3 draw away to Germany in a friendly last month.
Although with little chance of making Brazil, Paraguay now look capable of spoiling Argentina's hopes of securing their ticket to Brazil with two matches to spare.
Genes, thinking to the future, has mixed experience and youth in a revamped Paraguay side with veteran striker Roque Santa Cruz heading one goal and laying on another, and teenage defender Gustavo Gomez scoring on debut.
Midfielders Jonathan Fabbro, who struck first to give Paraguay a 1-0 lead at halftime, and Richard Ortiz also scored.
The top four teams in the nine-nation group qualify for the finals with the fifth-placed team go into a play-off against an Asian side for one more berth.