World Football - Weak Argentina win Copa warm-up
Both countries, warming up for the Copa America in Argentina in July, fielded teams made up of home-based players which in Argentina's case is virtually a third string.
Hauche opened the scoring in the ninth minute and added the third just before halftime following a fine run down the right by his Racing Club team mate Ivan Pillud, who beat two defenders before crossing from the goalline.
Striker Pablo Zeballos equalised for Paraguay in the 14th minute with a shot that took a deflection and central defender Federico Fernandez restored Argentina's lead in the 37th, heading home a free kick by midfielder Diego Valeri.
Defender Elvis Marecos reduced the deficit 11 minutes into the second half when he headed a corner inside the near post from a corner.
Winger Enzo Perez added Argentina's fourth in the 74th.
Argentina coach Sergio Batista has picked an intermediate squad of foreign-based players on the fringe of his first team for a tour of Nigeria and Poland next month as he looks to settle on his 22 players for the Copa America.
The squad, to meet Nigeria in Abuja on June 1 and Poland in Warsaw four days later, includes the likes of Manchester City's Pablo Zabaleta, 2010 World Cup defender Nicolas Otamendi of Porto and Palermo playmaker Javier Pastore.