David Villa saved Spain once again, hitting both posts before seeing his shot go into the net Saturday to give his team a 1-0 win over Paraguay and its first ever appearance in the World Cup semifinals.
With both sides having already missed penalty kicks, substitute Pedro Rodriguez hit the post following a pass by Andres Iniesta and the ball fell to Villa in the area. The striker took one touch before his curling shot hit the far post and then went in off the near post for his tournament-leading fifth goal.
In the semifinals, the European champions will face Germany in Durban on Wednesday.
Paraguay's defence mostly kept Spain's vaunted attack at bay, and both teams' best chance to win in normal time came from the spot.
Spain goalkeeper Iker Casillas saved a 59th-minute penalty kick by Oscar Cardozo. Paraguay captain Justo Villar matched him two minutes later, but only after referee Carlos Batres made Xabi Alonso retake an initially successful kick because of encroachment by several teammates.
Substitute Cesc Fabregas was brought down by Villar as he pushed the rebound past the goalkeeper, but Batres waved away appeals for another penalty.
Paraguay almost equalized in the 89th as Casillas stopped a shot by Lucas Barrios before punching away Roque Santa Cruz's attempt from the rebound. Villa then had a chance to make it 2-0 at the other end after a breakaway but Villar made the save.
Paraguay, playing in its first ever World Cup quarterfinal game, matched Spain for chances until the European champions improved after Fernando Torres made way for Fabregas in the 53rd.
Casillas easily saved Jonathan Santana's first-minute shot but could do nothing about Nelson Valdez's 41st-minute close-range finish. Valdez swept the ball into the net but his effort was ruled out for an offside, with replays showing that Cardozo had strayed as the crucial pass came forward.
Spain had to wait until the 34th for its trademark one-touch passing to create an opening. Villa, getting into the game after a spell of isolation on the left, surged up the middle and passed wide right to Iniesta, who hit a curling cross that only just eluded Torres and went out the other side.
Until then, Spain's best opening had been an individual effort by Xavi Hernandez. With his back to goal, Xavi flicked the ball into the air, spun 180 degrees and hit a 25-meter (yard) dipping shot that just cleared the bar.
Otherwise, Spain made only two first-half forays of note into Paraguay's area. Villa beat a challenge on left but his cross was easily cut out as Paraguay defended in numbers. Torres did the same on the right a minute later but immediately lost the ball in the area as his touch continued to betray him.
But the game immediately opened up with Fabregas' arrival.
Paraguay was awarded its penalty when Spain defender Gerard Pique grabbed Cardozo's arm with both hands and pulled the striker back as the pair awaited a cross into the area.
Spain then got its penalty when Antolin Alcaraz was ruled to have knocked down Villa.
Paraguay: Justo Villar, Dario Veron, Claudio Morel, Oscar Cardozo, Edgar Barreto (Enrique Vera, 64), Antolin Alcaraz, Jonathan Santana, Paulo Da Silva, Victor Caceres (Lucas Barrios, 84), Christian Riveros, Nelson Valdez (Roque Santa Cruz, 72).
Spain: Iker Casillas, Sergio Ramos, Joan Capdevila, Carles Puyol (Carlos Marchena, 84), Gerard Pique, Sergio Busquets, Xabi Alonso (Pedro Rodriguez, 75), Xavi Hernandez, Andres Iniesta, David Villa, Fernando Torres (Cesc Fabregas, 56).