Casillas saved a penalty from Paraguay's Oscar Cardozo and made a crucial double block at the end of Spain's 1-0 win to thwart attempted equalisers by Lucas Barrios and Roque Santa Cruz.
"Casillas has been extraordinary. He made two magnificent stops and he certainly contributed to our success," Spain coach Vicente del Bosque told reporters after the match.
Striker David Villa's goal with seven minutes remaining at Ellis Park sent Spain through to a last four clash with Germany, who thrashed Argentina 4-0 earlier in the day.
Casillas's 59th-minute penalty save had, however, crucially kept the scores at 0-0 when a goal would have been a big blow to a Spanish side that had the bulk of possession but could not find a way through a well-organised Paraguay defence.
Casillas said after the game that reserve goalkeeper Pepe Reina had told him which way to dive, suggesting Cardozo would not go the same way as he did in the penalty shootout with Japan.
"The match was enough to give you a heart attack. A lot of thanks go to Reina who told me which way he was going to shoot," he said.
Spain's team and bench rushed onto the field and mobbed Casillas at the end of the game.
Paraguay coach Gerardo Martino echoed Del Bosque's comments on the Real Madrid keeper, saying Spain's captain played a key role in his side's defeat.
"Undoubtedly he has been decisive," he said.
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