Defending champions Argentina needed two goals in extra time to subdue Switzerland 3-1 on Saturday night and advance to a semi-final clash against England.
Alexis Mac Allister headed Lionel Messi's corner kick into the net past Switzerland goalkeeper Gregor Kobel to give Argentina the advantage after 10 minutes.
But the Swiss refused to roll over.
They dug in and a period of dominance in the second half was rewarded when Ricardo Rodriguez slipped a pass to Dan Ndoye in the penalty area.
The Swiss winger slid a right-footed shot under the Argentina goalkeeper Emiliano Martinez to level proceedings at 1-1 midway through the second half.
Switzerland reduced to 10 men
But before the Swiss could fray Argentine nerves, they were reduced to 10 men. Breel Embolo was shown a yellow card for pretending he had been fouled and was sent off for his second bookable offence of the evening.
One man down, the Swiss forced the tie into 30 minutes of extra time. And they only cracked in the second 15 minutes.
Julian Alvarez collected the ball on the left-hand side of the Swiss penalty area and curled a shot past Kobel into the top right-hand corner to give Argentina the lead again.
Lautaro Martinez added the gloss of the 3-1 scoreline in the dying seconds as Switzerland chased the equaliser that could have sent the quarter-final into a penalty shootout.
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"We're among the best four in the tournament," Alvarez said. "So we're meeting our objectives.
"We knew it wasn't going to be easy. The whole match was hard, and we would have loved to have had the win earlier.
"The opponent was really good but we fought until the end, and finally the goals came."
With Argentina and England joining Spain and France in the semi-finals, it is the first time the top four teams in the Fifa rankings have all advanced to the semis.
"We knew this could happen," said Argentina midfielder Thiago Almada. "Switzerland have top players who find very good positions.
"But we knew how to hold them up and we've made it through."
Argentina will take on England, who saw off Norway 2-1 in Miami. Jude Bellingham scored both England goals after Andreas Schjelderup's 36th-minute opener for Norway.
