It was just the result coach Gerardo Martino was looking for after the draw with reigning world champions in their opening game.
Vera made the breakthrough in the 27th minute after a spell of sustained pressure at the Free State Stadium. Paraguay then squandered a number of good chances to extend their advantage before Riveros added a second with five minutes to go.
It is Slovakia's first appearance in the finals and they are heading for an early exit. The team's only effort of note came in stoppage time when substitute Filip Holosko's shot was turned over the bar by goalkeeper Justo Villar.
Paraguay dictated the pace from the start and Manchester City striker Roque Santa Cruz, who returned after a minor injury, came close to scoring twice. He almost gave his side the lead in the third minute, his effort turned away at the post by Everton-bound goalkeeper Jan Mucha. Then Nelson Valdez turned quickly but saw his effort go wide before play switched back down the other end.
Marek Hamsik played the ball out to Jan Durica but he sent his shot over the bar. Paraguay were having the majority of possession and Paulo Da Silva was only inches away from making contact at the back post following a free-kick by Claudio Morel.
Then Cristian Riveros drilled a shot from the edge of the area but Mucha was equal to it before Lucas Barrios was off target from an acute angle.
Slovakia again found themselves on the back foot in the 24th minute but Valdez fired wide. Paraguay's pressure paid on the 27th minute when they made the breakthrough. Barrios released Vera and he got the better of Durica to hook the ball home.
Slovakia hit back and Kornel Salata headed over the bar from inside the area in the 37th minute. It proved brief respite, however, with Santa Cruz almost adding a second a minute later only for Mucha to boot the ball clear.
Slovakia tried to step up the tempo at the start of the second half but Paraguay looked well in control. Vera should have scored his second goal of the game in the 72nd minute following a swift counter attack. However he steered a header wide in front of the posts following a cross and some good skill from Santa Cruz, who was unhappy at some of his treatment from Liverpool's Martin Skrtel.
Then substitute Aureliano Torres saw his effort take a deflection off a Slovakia defender and finish high over the bar.
Paraguay extended their advantage in the 85th minute when Da Silva played the ball into Riveros and he curled a shot into the corner.