Oscar Cardozo hit the winning penalty shot Tuesday in Pretoria, after the match remained scoreless through regulation and 30 minutes of extra time.
No Asian country has ever beaten a South American team at the World Cup in 14 attempts.
In the final match of the second round, Spain defeated Portugal 1-0 to move on to the quarterfinals.
David Villa scored the only goal in Cape Town. The Barcelona star scored on his own rebound in the 63rd minute following a save by Portuguese keeper Eduardo. It was the striker's 4th goal of the tournament.
Portugal created several scoring opportunities in the 2nd half but was unable to score an equalizer.
The European champions will play Paraguay in the final-eight on Saturday.
The final of the 2010 FIFA World Cup is July 11 in Johannesbur
European champions Spain reached the World Cup quarter-finals on Tuesday with a 1-0 win over Portugal, sending Cristiano Ronaldo, the world's most expensive player, heading moodily to the exit.
Spain, for whom star striker Fernando Torres was again overshadowed by goal scorer David Villa, will tackle Paraguay in Johannesburg on Saturday for a semi-final spot after the South Americans defeated Japan 5-3 in a penalty shoot-out.
New Barcelona signing Villa scored his fourth goal of the World Cup in the 63rd minute of an absorbing Cape Town encounter that also saw Portugal's Ricardo Costa sent off.
"Fernando worked hard as we all have over the past month. The substitution was made because Torres had done a lot of running and we needed fresh legs," said Del Bosque.
"Llorente had a very good final half-hour. It wasn't a change of tactics. Llorente gave us vitality."
Ronaldo left the stadium refusing to talk to reporters.
"We marked Ronaldo well and neutralised his threat," said Del Bosque.
Portugal coach Carlos Queiroz admitted: "Spain had the better chances and deserved to win."
For Paraguay, it was fourth time lucky after last-16 exits in 1986, 1998 and 2002.
"Argentina still have a great chance, Brazil as always in the World Cup are getting better and we're also there trying to do things right," said Paraguay coach Gerardo Martino.
After a largely sterile and goalless 120 minutes at Loftus Versfeld stadium, the first five penalties went in before luckless Japan defender Yuichi Komano aimed too high and the ball struck the crossbar before flying over.
That left Paraguay two successful kicks away from glory and Nelson Valdez and extra-time substitute Oscar Cardozo calmly slotted their kicks past Eiji Kawashima.
Meanwhile, FIFA president Sepp Blatter, under pressure to rethink his opposition to goal-line technology and video replays, apologised to England and Mexico after referee blunders featured prominently in their last 16 defeats.
Blatter was reacting to a legitimate Frank Lampard goal that was disallowed at the crucial stage with England trailing Germany 2-1 on Sunday and pressing hard just before half-time.
Television replays showed the ball landing well over the line before it bounced back into the hands of Manuel Neuer, who cleared and the Uruguayan referee Jorge Larrionda waved play on with Germany finishing 4-1 victors.
A few hours later Carlos Tevez headed Argentina in front from an offside position en route to a 3-1 win over Mexico and the situation was inflamed by the crowd seeing a big-screen replay.
Blatter told a news conference that apologies to English and Mexican officials had been accepted and said the technology debate would reopen at a July 21-22 meeting in Cardiff.
He stressed that only goal-line technology would be discussed, and this would not have offered any assistance to Roberto Rosetti, the Italian referee of the Mexico match.
Neither Larrionda nor Rosetti were on the list of officials who are staying on for the quarter-finals that was released later by FIFA.
Referees defended themselves at an open training session north of Pretoria with spokesman Jose Maria Garcia Aranda labelling World Cup match officials "excellent".
"We have to look at 54 matches and the decisions the referees have made in them," he said, adding sarcastically, "apparently the referees took only four or five decisions in these 54 matches and all of them were controversial."
