Spanish pundits highlighted the contribution of Fernando Morientes, who scored twice after coming on to replace Diego Tristan for the second half.
"[Coach Jose Antonio] Camacho wanted to add width to the attack and did so with the substitutions, As newspaper reported. "Spain also gained strength down the middle."
The joy in Spain at qualification for the next round was all the greater because the national team crashed out in the group stages in France four years ago.
In South America, however, "the first half dream turned to harsh reality in the second," according to Paraguay news daily ABC.
"The red and whites are close to saying goodbye," the paper continued before praising Camacho for his substitutions.
"Spain needed a change and made it a reality with Fernando Morientes and Ivan Helguera," ABC said.
Paraguay must now beat Slovenia on 12 June in Sogwipo to stand any chance of qualifying.