Switzerland beat Colombia 4-3 in a penalty shootout in Vancouver, Canada, on Tuesday to reach the quarterfinals of the World Cup for the first time since 1954.
Colombia faltered when Davinson Sánchez smashed his spot kick against the bar and Cucho Hernández had his effort saved by goalkeeper Gregor Kobel, before Rubén Vargas scored to book a quarterfinal date with defending champion Argentina.
"They had the crowd on their side, so it was a tough game for us," Kobel said. "We know we had some stretches of the game where we had to defend and stay strong mentally. Obviously we had a few players missing so, yeah, it was a big challenge for us."
The sides were tied 0-0 after extra time.
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It is the first time Switzerland have won multiple knockout games in the same World Cup, and their first time in the last eight since they hosted the tournament 72 years ago.
Colombia were looking to advance to the quarterfinals for the second time and first since 2014 when they fell to hosts Brazil. They have now been eliminated on penalties in their past two World Cup appearances, after falling to England in the round of 16 in 2018. They failed to qualify for the last tournament in Qatar four years ago.
"The dream was enormous," Colombia midfielder John Arias said. "The country showed us that it believed in us, that it lived every moment with us, and I think that only makes the pain even greater."
Colombia twice came close to winning the game in extra time. Jhon Lucumí sent a header against the crossbar before Jáminton Campaz shot over the bar with only the goalkeeper to beat following a defensive miscue from Granit Xhaka.
"Clearly, something is missing. We haven't been able to win with the national team," Arias added. "We all want to win. We all want to achieve important things with the national team because I think the people deserve it.
"I think it's something we need to reflect on carefully, and hopefully we'll find what it is that's still missing."
Switzerland were missing World Cup breakout star Johan Manzambi because of an injury suffered in training Monday. The 20-year-old midfielder scored three goals and added two assists in Switzerland's first four World Cup matches.
Vargas, who has scored two goals in the World Cup, also left Monday's training early but was available off the bench and came on in stoppage time at the end of regulation before scoring the decisive penalty.
The Swiss reached the round of 16 at the past three World Cups but failed to advance with a smaller field of 32 teams.
Argentina now await in Kansas City, Missouri, on Saturday after they fought back to beat Egypt 3-2 in a dramatic finale earlier Tuesday.
FIFA president Gianni Infantino was among those at BC Place, where the sellout crowd was overwhelmingly clad in yellow in support of Colombia.
The match was tightly contested by two teams with contrasting styles, the Swiss with a more organized approach and Colombia more attack oriented. Switzerland had a slight edge in possession.
As well as Manzambi, the Swiss were also without Luca Jaquez and midfielder Michel Aebischer. Colombia were missing forward Jhon Córdoba, who was injured in the team's round-of-32 win over Ghana.
Gustavo Puerta had the first good chance for Colombia with a shot from distance in the 21st minute that was pushed away by Kobel.
The Swiss got one of their best opportunities in the 30th with Fabian Rieder's blast at Camilo Vargas, who punched the ball down. Minutes later, Vargas smothered another attempt from Dan Ndoye.
The Swiss had a free kick in the 52nd minute, but Rieder's attempt curled around the wall and went into the side netting.
The Associated Press contributed to this report.