Mexico ended their 40-year wait for a World Cup knockout win, while Erling Haaland sent Norway through and Kylian Mbappé fired France into the last 16.
Mexico reached the World Cup last 16 with a 2-0 win over Ecuador at the Azteca Stadium, their first knockout-stage victory in the tournament for 40 years.
First-half goals from Julian Quinones and Raul Jimenez put the co-hosts in control, and although Ecuador saw more of the ball after the break, Mexico stayed organised and kept another clean sheet.
They will face either England or DR Congo on Sunday.
With Norway on the ropes and the match heading for extra time, Erling Haaland came to his side's rescue, scoring four minutes from time to secure a 2-1 victory over Ivory Coast in Dallas.
Antonio Nusa gave Norway the lead in the first half with a fine curling finish after cutting in from the left and finding the far corner.
But Ivory Coast continued to apply pressure and were rewarded in the 74th minute when Manchester United forward Amad, who had been introduced just after the hour mark, capped a brilliant solo run with the equaliser.
Having scored four goals in his first two group games before being rested for the third, Haaland had been one of the tournament's standout players. But for much of the match against Ivory Coast he struggled to make an impact.
Then, with extra time looming, he struck the winner.
"I was dead tired, so I thought, 'I can't cope with extra time, so we have to score,'" Haaland said after the match.
The Manchester City striker's goal secured Norway's first-ever World Cup knockout victory. They will now face Brazil in the last 16 in New York this weekend.
Mbappé scored twice as France beat Sweden 3-0 in New York to book their place in the last 16.
The French forward is now one goal behind Lionel Messi on the men's all-time World Cup scoring list. He could also have completed a hat-trick, but another effort was ruled out for offside.
Sweden coach Graham Potter said before the match that his side would need to produce their best performance of the tournament to stand a chance against heavily favoured France, but they fell well short.
Mbappé broke the deadlock just before half-time, setting France on course for a comfortable victory.
Michael Olise provided the first of his two assists when Bradley Barcola doubled France's lead shortly after the break, before setting up Mbappé again in the 74th minute to complete the scoring.
Les Bleus will face Paraguay in Philadelphia after the South Americans stunned four-time champions Germany on penalties following a 1-1 draw.
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