The USA beat Iran 1-0 in a battle of geopolitical foes to reach the knockout phase of the World Cup on November 29 while England eased through against Wales.
The Americans earned a second round meeting with the Netherlands after Christian Pulisic bundled the ball into the net in the 38th minute of an absorbing contest in Doha.
Only the third international meeting of the bitter ideological rivals had been marked by a bad-tempered buildup.
Iran's Football Federation had on Sunday demanded that FIFA punish US Soccer for posting a modified version of their country's flag on social media.
Meanwhile the Iran team's every move in Qatar has been scrutinised for signs the players are showing support for mass anti-government protests that have shaken the Islamic republic.
On Tuesday, having opted not to do so in their opening match, the Iranian players did sing the national anthem, albeit without much enthusiasm, in the highly-charged atmosphere of the Al Thumama Stadium.
There was nothing half-hearted about the Iranians' performance though, but the Americans were deserved winners after digging deep for the victory.
"The guys grinded, gave every single ounce and we are undefeated going into the next round," USA coach Gregg Berhalter said.
Iran substitute Saman Ghoddos wasted two clear scoring opportunities.
"The dream is over," Iran coach Carlos Queiroz said. "Unfortunately football always punishes the team that doesn't score."
Reflecting the fact that the game was about more than sport, US President Joe Biden had wrapped up a speech on the economy in Michigan, but returned to the stage to tell the crowd: "The US one, Iran zero! The game's over!"
England end Welsh challenge
England's task was easier, as they swept past Wales 3-0 to win Group B and set up a meeting with Senegal in the early hours of December 5 (2am Cambodian time).
After an uneventful first half in the Ahmad Bin Ali Stadium, Marcus Rashford and Phil Foden pounced in the space of two second-half minutes to effectively end the contest.
Manchester United forward Rashford then added his second goal of the night to ensure Wales' first involvement in a World Cup finals since 1958 ended in disappointment.
"This is what I play football for, the biggest moments, the best moments," Rashford said.
"I'm really happy today that we're going through to the next round. I have massive ambition for this team and think we can play even better than we showed today."
The Netherlands cruised into the last 16 with a comfortable 2-0 win over already-eliminated Qatar to win Group A.
Cody Gakpo netted his third goal of the tournament and Frenkie de Jong scored the other as the Dutch easily beat the host nation at Al Bayt Stadium.
There was more excitement at the Khalifa International Stadium where Kalidou Koulibaly's first goal for Senegal pushed his country to a 2-1 win over Ecuador and a place in the knockout phase for just the second time in their history.
The Chelsea defender's 70th-minute strike eliminated the South Americans, who had only needed a draw to go through, and made Senegal the first African side to progress from the group stage so far in this tournament.
Meanwhile, an Italian man who ran onto the pitch during Monday's game between Portugal and Uruguay carrying a rainbow flag was released following a brief detention.
The man identified as Mario Ferri also wore a T-shirt with the words "Respect for Iranian Woman" on the back and "Save Ukraine" on the front.
Ferri said on Instagram: "FIFA banned rainbow captain's armbands and human rights flags in the stands, they blocked everyone, BUT NOT ME."
Ferri has staged similar protests before, including at the 2014 World Cup in Brazil, where he raised the issue of children living in poverty.