(Reuters) - Argentina scored in the 118th minute to beat Switzerland and Belgium clung on to defeat the United States in another heart-stopping period of extra time to reach the World Cup quarter-finals amid more extraordinary drama on Tuesday.

Angel Di Maria struck with two minutes of the extra period remaining to give Argentina a 1-0 win over stubborn Switzerland, who still had time to hit the post amid unbearable tension in Sao Paulo.

Belgium took a 2-0 extra-time lead through Kevin De Bruyne and Romelu Lukaku but, after Julian Green pulled one back, they had to survive an extraordinary end-to-end finale as the U.S. threatened an equalizer before winning 2-1.

"Football is brutal, brutal, brutal. Unfortunately, we didn't quite have enough strength at the end to get through extra time," Switzerland's assistant coach Michel Pont told reporters as the tournament continued to surpass itself for drama and emotion.

Argentina and Belgium will meet in Brasilia on Saturday (1600 GMT) after completing a quarter-final line-up which will feature all eight group-stage winners with four teams each from Europe and Latin America.

Hosts Brazil face Colombia in Fortaleza on Friday (2000), preceded by France against Germany in Rio de Janeiro (1600) and the Netherlands take on rank outsiders Costa Rica in Salvador on Saturday (2000).

The Dutch, runners-up four years ago, will almost certainly be without hard-tackling midfielder Nigel de Jong for the rest of the tournament after he was ruled out for two to four weeks with a groin injury.

Off the field, Cameroon's football federation (FECAFOOT) said it would investigate claims that seven players were involved in match-fixing at the World Cup, centered on the 4-0 defeat by Croatia when Alex Song was sent off in the first half.

"Recent allegations of fraud around Cameroon's three 2014 World Cup games, especially Cameroon v Croatia, as well the existence of "seven bad apples (in our national team)" do not reflect the values and principles promoted by our administration," FECAFOOT said in a statement.

The allegations against Cameroon came from convicted fraudster Wilson Raj Perumal, who it emerged during a discussion with German magazine Der Spiegel had accurately forecast the result and the fact that a player would be sent off

PENALTIES LOOMING

Twice champions Argentina dominated the last-16 game against Switzerland but their attacks lacked variety and too often ended with hopeful crosses into the penalty area.

Switzerland were expertly marshaled by veteran coach Ottmar Hitzfeld who had already announced that he would retire after the tournament.

With penalties looming, Angel Di Maria stroked the ball home from the edge of penalty area to put the finishing touch to a trademark Lionel Messi run, sparking wild celebrations among the South American team and their fans in Sao Paulo.

The celebrations nearly proved premature when Swiss substitute Blerim Dzemaili headed against the post from point-blank range and the ball rebounded on to his knee and went centimeters past the post.

With goalkeeper Diego Benaglio joining the attack, Switzerland won a free kick on the edge of the area but, amid extraordinary tension and with Argentine substitutes praying on the bench, Xherdan Shaqiri sent his effort into the defensive wall

"It was a game that we deserved to win in 90 minutes," Argentina coach Alejandro Sabella told reporters.

"It was even during a first half in which they had two clear chances to score, but in the second half we were clearly superior, we had five or six shots at goal and in extra time we also had more chances."

Belgium dominated normal time and were frustrated by an inspired Tim Howard in the U.S. goal but struck early in extra-time when De Bruyne collected the ball before turning and firing home an angled shot from seven meters.

Substitute striker Lukaku powered home a second on 105 minutes after a clever De Bruyne pass before Green's volley at the start of the second period set up a pulsating finale in which Clint Dempsey almost sneaked an equalizer.

The U.S. could have sealed it at the end of normal time but substitute Chris Wondolowski skewed his effort horribly wide from five meters.

"We had about 15 chances, we were controlling the game I think it is largely deserved even though at the end we conceded one," Belgium coach Marc Wilmots told reporters.

Howard felt heart-broken to lose.

"We left it all out there but we lost to a really good team. It hurts but hats off to Belgium they were fantastic," he said.