The three-times European champions’ keeper Unai Simon saved from Switzerland’s Manuel Akanji and Fabian Schar while Ruben Vargas hammered his shot over the bar.
Spain’s Sergio Busquets and Rodri squandered their kicks but Gerard Moreno and Dani Olmo converted, leaving it for Mikel Oyarzabal to strike the decisive spot-kick in St Petersburg.
That helped erase the memory of defeat on penalties to hosts Russia in Moscow at the 2018 World Cup, and came after a terrible run from the spot which had seen Spain miss their last five penalties, including two earlier in the tournament.
In normal time, Spain took an eighth-minute lead when a Jordi Alba strike took a heavy deflection off Daniel Zakaria and went into the net. It was the 10th own goal of the tournament – more than at all the other Euros combined.
Hoping to win their first of four quarter-final appearances in major tournaments, Switzerland deservedly levelled in the 68th minute when Xherdan Shaqiri cashed in on a mix-up in the Spain defence.
The Swiss cause was complicated by Remo Freuler being shown a straight red card in the 77th minute, yet they held on to force the extra period and somehow survived a Spain onslaught to make it to spot-kicks.
Despite beating France 5-4 on penalties in the last 16 by scoring all their kicks, only Mario Gavranovic could beat Simon and the Swiss were left heartbroken.
Spain, though, are rewarded with a trip to London’s Wembley Stadium to face either Belgium or Italy and are dreaming of a first major final since winning Euro 2012.
“I knew I couldn’t miss and luckily the ball went in. On the way to the spot many things went through my head but I knew exactly what to do,” said Spain forward Oyarzabal.
|Soccer Football – Euro 2020 – Quarter Final – Switzerland v Spain – Saint Petersburg Stadium, Saint Petersburg, Russia – July 2, 2021 Spain’s Rodri misses a penalty during a penalty shootout. Pool via Reuters
While Spain prevailed, this was an extraordinary effort from Switzerland, who ended the game without their three best midfielders as Granit Xhaka was suspended, Freuler had been sent off and then Shaqiri hobbled off injured.
Swiss keeper Yann Sommer then produced more heroics to add to his superhuman efforts against France, making save after save as Spain overwhelmed their opponents in extra time but failed to score.
“I’m so proud of the team, what we’ve achieved here with the whole country behind us,” said Sommer.
Both sides had overcome important psychological barriers in the last round, Spain beating Croatia 5-3 in an epic encounter to earn their first win in a major tournament knockout tie since lifting Euro 2012.
Switzerland’s shootout success over France, meanwhile, which came after scoring two late goals to draw 3-3, was their first triumph in a knockout match since 1938.
But the teams seemed drained from their efforts and there was little drama in the opening hour as Switzerland nullified Spain’s passing game with a relentless high press and Luis Enrique’s side could only find a breakthrough with the own goal.
Switzerland became more ambitious in the second half and nearly levelled when Zakaria landed a header inches wide post. Moments later, Simon thwarted Steven Zuber at the near post.
They finally equalised when Spain defenders Aymeric Laporte and Pau Torres collided and Freuler laid the loose ball into the path of Shaqiri, who coolly slotted into the bottom corner.
But Vladimir Petkovic’s side were on the back foot again when Freuler landed a high tackle on Moreno and was sent off.
Spain were utterly dominant in extra time and Moreno missed three clear efforts. Sommer made fine saves to keep out efforts from Alba and Oyarzabal while defender Ricardo Rodriguez made a brave block to thwart Marcos Llorente.
Spain brushed aside their frustration though to win the battle of nerves from the spot, keeper Simon coming out on top to wipe the memory of his disastrous gaffe in the previous game against Croatia.
“Football has been fair to us as we are the deserved winners,” added Simon.