The Americans will continue their bid to defend their world title against Spain in Reims on Monday after a win that saw them make it 18 goals for the tournament and break the 24-year-old record for the number of goals scored in the group stage held by Norway.
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Lindsey Horan opened the scoring when she tapped home Samantha Mewis' flick with two minutes on the clock, and Tobin Heath helped make sure of the points by firing past Hedvig Lindahl via a big deflection off Jonna Andersson four minutes after the break.
Andersson's own goal somehow survived a VAR check from referee Anastasia Pustovoytova despite substitute Carli Lloyd looking to be offside in the build-up.
However afterwards Lloyd claimed she hadn't seen the incident, with Heath saying that she would "take the goal" all the same.
Lloyd replaced star player Alex Morgan at half-time after the 29-year-old took a knock in the opening 45 minutes, but USA coach Jill Ellis was non-committal on whether she would be fit for Spain.
"Alex took a knock in the first half and it was more of let's be smart about this, in terms of what we did," she said.
"It's a zero risk game in terms of having players available in the next round."
Sweden started with a team with seven changes from the side that beat Thailand 5-1 last time out and four players making their World Cup debut, and offered very little attacking threat.
However their defeat means that they face Canada next in Paris on Monday and are in an easier side of the knockout draw from the States, who have hosts France, England and Norway as potential opponents further down the line.
The only truly top draw side lined up for the Swedes is Germany, who they could meet in the quarter-finals if they beat Canada, who lost 2-1 to Group E winners the Netherlands earlier on Thursday.
Their coach Peter Gerhardsson admitted that he "didn't think in advance that it was important to end up first or second", but Ellis was unconvinced.
"I think after the game that might be a fair comment. I think that's not caring about the game but thinking ahead," she said.
There was heartbreak for Chile meanwhile, who needed to beat Thailand by three goals in order to pip Nigeria into the knockouts.
They were 2-0 up with five minutes left when they were awarded a penalty via VAR, only for Francisca Lara to crash her spot-kick off the bar and see her side knocked out.
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Just 10 seconds of the allotted five minutes of added time remained in Montpellier when Nchout curled her team into the next round as one of the best third-placed teams with a superb strike to beat New Zealand 2-1.
Nchout had earlier given Cameroon the lead in the 57th minute, controlling with her shoulder before slotting home.
However, when Aurelle Awona sliced a Katie Bowen cross into her own net with 10 minutes left, it looked as though both teams were heading out.
Instead, Nchout's last-gasp goal means Cameroon go through as one of the best third-placed sides, while New Zealand return home without a point.
The Netherlands will meet Japan in the last 16 after Lineth Beerensteyn turned in a Desiree van Lunteren cross in the 75th minute in Reims to seal their win over Canada and advance as Group E winners.
Veteran Canada forward Christine Sinclair scored her 182nd goal for her country on the hour mark following Anouk Dekker's 54th-minute opener, leaving her just two shy of Abby Wambach's international record for the United States, but it wasn't enough to beat their opponents to first place.
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