Casillas had been forced into just one real save in the match, when he beat away a snap shot from Park Ji-sung on 67 minutes.
A Morientes header gave Spain their first good chance on 27 minutes, goalkeeper Lee Woon-jae clutching the ball gratefully just under his crossbar.
South Korea were getting nowhere, as Ivan Helguera and Ruben Baraja created a formidable barrier in front of the defense and Spain gradually took control of the game.
With halftime approaching, Javi de Pedro flashed a left-foot shot just wide from 20m and in injury time Fernando Hierro rose highest in a crowded area to head over.
Spain thought they had taken the lead four minutes into the second half. De Pedro's free kick cross went in after hitting the back of Kim Tae-young as a group of players went up for a header but the goal was disallowed, apparently for off-side.
With both teams tiring, the match went into extra time and only two minutes into it, Morientes thought he had sent Spain into the semifinals.
Instead, the game went to penalties and the first seven were confidently converted before Joaquin's weak strike was saved by Lee Woon-jae diving to his left.
Victory for Hiddink's side over Germany would take them through to the Yokohama final on June 30. To get there they will almost certainly have to play better than they did yesterday, although Hiddink was in no rush to get to work on his preparation.
"We'll have a little glass of champagne now and what comes tomorrow comes tomorrow," Hiddink said.
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