YOKOHAMA, Japan, 18 June — Brazil struggled for an hour to impose their authority over Belgium yesterday before goals by Rivaldo and Ronaldo sent the World Cup favorites into the quarterfinals.

Brazil, eventual 2-0 winners, will meet England in a repeat of the celebrated 1970 World Cup encounter while the United States, who defeated Mexico by an identical scoreline, play Germany. "The Cup starts now," said a beaming Ronaldo, whose fifth goal of the tournament puts him equal top with Germany’s Miroslav Klose. "Every match is going to be a final. Now we must think about England."

Rivaldo, who struck the spectacular opening goal in the 67th minute, has scored four while the Brazilian team have accumulated 11 from four matches.

After romping through the first round, Brazil labored against their first European opposition in the form of a disciplined, tenacious Belgium side.

Only a controversial refereeing decision and a series of courageous stops from goalkeeper Marcos saved the four times world champions in the first half of the second round match played in the Japanese city of Kobe.

In the 36th minute, Marc Wilmots, who scored in each of Belgium’s three first-round matches, soared above Roque Junior to head an inswinging cross from Jacky Peeters into the net.

To the disbelief of the Belgium team, Jamaican referee Peter Prendergast disallowed the goal, apparently for pushing.

"We all thought the goal was valid, that (decision) changed the course of the match," said Belgium coach Robert Waseige. "But that’s football. I think this Brazilian defense can be beaten."

Ronaldo, whose hunger for goals is palpable after four injury-disrupted years since the last World Cup, had three good chances but could not break the deadlock.

Finally, Rivaldo unlocked the Belgium defense when he controlled a high pass from Ronaldinho on his chest with his back to the goal, brought the ball under control with his next touch before swiveling to crash it into the net.

Twenty minutes later, Ronaldo finally got on the scoresheet with a left-foot strike which put the result beyond doubt.

"We knew about the way Belgium would play with the high balls but we prepared for this and we were able to cope," said Brazil coach Luiz Felipe Scolari.

The United States, 3-2 conquerors of Portugal in the first round, again surpassed all pre-match expectations against neighbors Mexico in Chonju, South Korea, after failing to win a game four years ago in France.

"Our guys left everything on the field today," said coach Bruce Arena. "I’m very proud of them. It’s a great day for US soccer."

The United States reached the semifinals of the inaugural World Cup in Uruguay in 1930 but needed only two group games to qualify in a tournament snubbed by most of the leading European nations.

Brian McBride and Landon Donovan scored the American goals in a bad-tempered 47th encounter between the two old rivals which featured 10 yellow cards.

In a rivalry stretching back to 1934 Mexico have won 28 times, lost 10 and drawn nine. More significantly, though, the United States have won five of the last six meetings.

The purposeful, athletic American side were again quick on the counterattack and their first goal after only eight minutes was typical of their performances during the tournament.

Captain Claudio Reyna delivered a low cross to Josh Wolff who laid the ball back to McBride for the striker to score his third goal of the tournament with a crisp drive.

Mexico laid siege to the American goal where Brad Friedel, sometimes desperately but always successfully, scrambled the ball clear.

Midfielder John O’Brien was lucky to avoid conceding a penalty when he punched the ball in the 56th minute but, typical of Mexico’s luck, he was spotted neither by Portuguese referee Vitor Melo Pereira nor the linesman.

"We were unlucky, there was a very unfortunate decision by the referee," said Mexico coach Javier Aguirre.

Donovan scored the second US goal in the 65th minute after another breakaway against an increasingly frustrated Mexican side as the US fans chorused "Hey, hey hey, goodbye".

"We know each other and there’s been a lot of bad blood over the years," said Arena, a former international goalkeeper who coached the US team at the 1996 Atlanta Olympics. "But when the game’s over we’re friends again."

Arena had earlier spoken to President George W. Bush, who wished the team good luck. Reflecting growing interest back in the United States, Bush said the team’s performances had excited even "those of us who don’t know much about soccer".