Tournament top scorer Villa pounced with seven minutes left to net his fifth goal at the finals and set up a semifinal clash with Germany.
Spanish striker David Villa fired his team into the World Cup semifinals with a late goal to sink Paraguay 1-0 after both sides missed penalties in a dramatic encounter at Ellis Park on Saturday.
Tournament top scorer Villa pounced with seven minutes left to net his fifth goal at the finals, after his right-footed shot remarkably went in off both posts, to set up a last-four clash with Germany who had earlier thrashed Argentina 4-0.
"We're in the last four in the world. It's a good moment for Spanish football," said coach Vicente Del Bosque. "There were good things... but we weren't as at ease in possession as in other games and it's important to be comfortable."
Spain's captain and goalkeeper Iker Casillas, who saved a penalty from Paraguayan striker Oscar Cardozo, added: "This is no small achievement. My team-mates played a great game. This team, for all the quality we have, can go a long way."
The victory takes European champions Spain into the last four at the World Cup for the first time since 1950.
Paraguay's coach Gerardo Martino said: "We gave our all, we had opportunities, but unfortunately Spain scored and Paraguay didn't... We didn't have luck with us.
"It was a game where we showed we could have come out winners. Now we have to resign ourselves to this tough blow."
Until Villa's goal, the hard-working South Americans had successfully nullified Spain's normally dominant midfield and created the clearer chances in a closely fought first half.
The quarter-final burst into life shortly before the hour when Guatemalan referee Carlos Batres ruled that Spain defender Gerard Pique had hauled down Cardozo in the penalty area.
The striker sent his spot kick low to the left of Casillas but the goalkeeper went the right way and saved comfortably.
There was more drama at the other end of the pitch minutes later when Spain were awarded a penalty after Villa went down under a challenge from central defender Antolin Alcaraz.
Xabi Alonso netted high to Justo Villar's right, sparking celebrations on the Spain bench, but the referee made him retake it after players from both sides encroached into the area.
Alonso went low to Villar's left with his second attempt and after his shot was saved substitute Cesc Fabregas, on for the ineffective striker Fernando Torres, appeared to have been hacked down by the keeper, but the referee awarded only a corner.
As Spain pressed for a winner, midfielder Xavi, who went close with a fizzing volley in the first half, drove narrowly wide and Andres Iniesta drew another fine save from Villar.
Villa then popped up to grab the decisive goal in the 83rd minute from a rebound after substitute Pedro had hit the upright following a brilliant run by midfielder Iniesta.
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}
)
){kind=small}
){kind=small}
)
)
)
)
)
){kind=small}
){kind=small}
){kind=small}
){kind=small}
){kind=small}