Peru will meet either the United Arab Emirates or Australia, who play the Asian confederation playoff in Doha on June 7, for a place in Qatar. The inter-confederation playoff will take place in Doha on June 13 or 14.
Peru also had to go through a playoff to reach the last World Cup in Russia, defeating New Zealand over two legs to qualify for their first finals since Spain in 1982.
On Tuesday, Peru started the night with 21 points, one more than Colombia and two ahead of Chile, knowing that a win over Paraguay in the final round of qualifying would be enough to wrap up the playoff spot.
Three minutes before halftime it was 2-0, Cueva the architect again. His work outside a packed penalty box led to a cross finished off by Yoshimar Yotun.
Ricardo Gareca's side controlled the second half without making many more chances and were content to see the game out and send the capacity crowd at the National stadium into raptures at the final whistle.