Hungary, the most successful country in Olympic water polo and gunning for their fourth consecutive gold medal, opened the tournament with back-to-back losses to Serbia and Montenegro, but got back on track by beating Britain and Romania.
The win over the Americans showed there is plenty of life left in the Hungarian team.
"This is definitely the Hungary team of old," said U.S. captain Tony Azevedo, who was part of the team that lost in the Beijing final to Hungary.
Hungary's charismatic goalkeeper Zoltan Szecsi said the Olympic water polo tournament had now started for real.
"It's an easy trap, to play very well at the beginning and to get blown up by the end," he said, perhaps in a swipe at fierce rivals Serbia, who won Group B on the back of an unbeaten run.
The win lifted Hungary into second place, with the final group positions to be decided by Montenegro's game against Britain later on Monday.
"We are old, and we are the foxes," Szesci said.
"You know the tale of the fox and the bird with the cheese? The bird has the cheese and fox says, 'You sing very well. Oh yes? Yes, please sing for me. Lalala, and the cheese falls for the fox.'"
Serbia, who have dominated water polo's biggest competitions over the last four years but are still missing an Olympic gold, demolished Romania 12-4 earlier to win the group, which gave the team confidence, said Serbia's Filip Filipovic.
In Group A, Croatia defeated Kazakhstan 12-4 to top the pool, and with Montenegro expected to finish second in Group B, this year's tournament is being dominated by the states from the old federal Yugoslavia.
"Can you imagine if we didn't separate 20 years ago what could happen?" Filipovic joked.
Croatia also went through unbeaten from their pool, though it is regarded as the easier of the two groups, and centre forward Niksa Dobud said the knockout rounds were all that mattered.
"It don't mean nothing before the quarter-finals. If we lose there, we go home," Dobud said.
Australia stunned Greece 13-8 in their final group stage match, also on Monday, to book their place in the quarter-finals.
Australia had been languishing in fifth after a solitary victory over Kazakhstan, but the win saw them shoulder Greece out of the fourth and final qualification spot.
Australia, playing in green and gold caps against the white of Greece, raced away midway through the game and Greek captain Georgios Afroudakis had no complaints about the result.
"They deserve to go to the last eight," Afroudakis, appearing at his fifth Olympics, said. "We go back home unhappy, but that's sport."
- Serbia and Montenegro