The United States' exit gives England a golden opportunity to win the Women's World Cup but they face a tricky encounter with Nigeria on Monday in the last 16, before co-hosts Australia face Denmark.
The Americans' hopes of winning an unprecedented third World Cup in a row were ended on penalties by Sweden in a night of drama in Melbourne on Sunday.
European champions and fourth-ranked England have never won the World Cup, but Sarina Wiegman's side are now the favourites.
Jamaica or Colombia, who play on Tuesday, await in the quarterfinals.
But first England must avoid falling to a shock defeat by 40th-ranked Nigeria when they kick off at 0730 GMT in Brisbane.
Wiegman vowed on the eve of the match that there would be no complacency from her side, especially given that this World Cup has witnessed so many surprises.
"What we've seen in this tournament is that nothing is easy," said Wiegman, who took her native Netherlands to the 2019 final before losing to the United States.
England started with an underwhelming 1-0 win over debutants Haiti and then saw off Denmark by the same scoreline, before hammering China 6-1 in their last group game.
Chelsea forward Lauren James scored twice and set up three more to announce herself to a global audience.
Key midfielder Keira Walsh was stretchered off after hurting her knee against Denmark but the injury was not as serious as initially feared and she could play against Nigeria.
The Super Falcons are one of the stories of the World Cup, having overcome rows with their federation over bonuses to beat Australia 3-2 in the group stage.
Their American coach Randy Waldrum believes knocking England out would be "transformational" for the sport in the country.
"Already with what we have accomplished Nigeria is buzzing again, from what I understand," he said.
KERR POISED TO RETURN
At 1030 GMT, Australia play Denmark in front of what could be a bumper crowd of more than 70Â 000 at Stadium Australia in Sydney.
A quarterfinal against the winner of Tuesday's game between France and Morocco awaits.
Australia coach Tony Gustavsson has hinted that talismanic striker Sam Kerr will play a part against the Danes.
The Matildas captain has yet to see any minutes at the tournament after a calf injury she sustained before their opening game.
But she took a big step towards her recovery by resuming training with a ball on Saturday and could finally be thrust into action.
"We had a nice moment with the team yesterday to see her back with her boots on and touching the ball and being with the team in training," said Gustavsson on Sunday.
"It was a very good feeling for Sam, her teammates and me."
Australia beat Denmark 3-1 in a friendly last year, but Gustavsson is wary of the threat posed by a side that England found hard to break down.
"They have threats left and right and in very different ways," he said.
"It's going to be tough and we need to bring our A game."
The first two quarterfinals will see Sweden face Japan and the Netherlands take on Spain, both on Friday.