Brazil beat Saudi Arabia 3-0 in Barranquilla, while Spain narrowly escaped a shock defeat by South Korea , winning a penalty shootout 7-6 after 0-0 draw in regulation and extra time in Manizales.
Four-time champion Brazil struggled in the first half but scored three goals in the second period to clinch its spot in the quarterfinals. Striker Henrique scored in the 46th minute, Gabriel Silva added to the lead in the 69th and substitute Dudu sealed the victory in the 86th.
''Now we have to think about Spain, it's going to be an interesting match,'' Brazil coach Ney Franco said. ''Two of the tournament's best teams playing against each other. Both are here to fight for the title.''
In the other quarterfinal matches, it will be Argentina vs. Portugal, Colombia vs. Mexico and Nigeria vs. France.
Spain struggled against South Korea and just barely avoided an upset. The Spaniards had won all of its matches so far but were not able to get past the South Korean defense in regulation and extra time.
South Korea's Kim Kyung-jung missed the deciding penalty, firing over the crossbar. Spain goalkeeper Fernando Pacheco had stopped South Korea's third attempt, by Lee Ki-je, while Koke missed Spain's only shot over the crossbar.
Spain is trying to win second U-20 title to add to its first trophy in 1999. South Korea's best showing had been a fourth-place finish in 1983.
In Cartagena, Antoine Griezmann scored in the 75th to give France a 1-0 victory over Ecuador. Griezmann tapped the ball home after Ecuador keeper John Jaramillo made the initial save but failed to control the rebound.
Earlier in Armenia, Nigeria advanced with a close-range goal by striker Edafe Egbedi in the 52nd in front of nearly 20,000 fans at the Centenario stadium.
''It was a difficult match but we were the ones who took more risks,'' said Nigeria coach John Obuh, who was wearing a Colombian sombrero and earned the support of the local fans. ''The English team played very defensively.''
England, playing without many of its top players, is winless in 14 straight matches at the Under-20 World Cup, a streak dating back to the tournament in Malaysia in 1997. More than 30 eligible English players were not released by their clubs for the tournament.
''If you look at the results, you can say it was a failure,'' England coach Brian Eastick said. ''The only way to change that is to change regulations to make the clubs release their players.''
Argentina, trying to win a record seventh world title, advanced Tuesday by beating Egypt 2-1 with two goals by Roma midfielder Erik Lamela in Medellin. Colombia was losing to Costa Rica but rallied to win 3-2 on a stoppage-time penalty by Porto playmaker James Rodriguez. Portugal edged Guatemala 1-0, while Mexico got past Cameroon on penalties after a 1-1 draw.
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