A Jude Bellingham overhead kick deep in injury time and a Harry Kane strike early in extra time allowed England to beat Slovakia 2-1 in their last-16 tie in Gelsenkirchen.
It was very nearly another ignominious exit for England that would have rivaled their defeat by Iceland at the same stage of Euro 2016.
They fell behind to Ivan Schranz's 25th-minute goal for Slovakia and were on their way out of the competition as a Phil Foden equalizer was disallowed for offside.
But Bellingham's moment of inspiration five minutes into stoppage time at the end of the game saved Gareth Southgate's side, as the Real Madrid man acrobatically turned home Marc Guehi's flick-on from a throw-in.
Slovakia's resistance was broken, and England got what proved to be the winner a minute into the extra period.
Substitute Ivan Toney headed Eberechi Eze's mishit shot back across goal for Kane to power home his second goal of the tournament.
That set up a quarter-final meeting with Switzerland on Saturday in Duesseldorf.
"That's the desire and the attitude from the boys. It looked tough for a second there but you keep going," said Kane. "Jude does what Jude does and what an unbelievable goal."
"We want to be better," admitted Southgate. "I'm not going to hide from that but the spirit and character was there for everybody to see and we're still in there fighting."
Slovakia coach Francesco Calzona said he was proud of his team despite the defeat.
"My team showed a lot out there. They were great, gave away very little and came close to going through," said the Italian.
"And in extra time we were in their half for long periods, I'm very proud."
Georgia give Spain scare
There was also a scare for Spain in the late game in Cologne, as they fell behind against Georgia when Robin Le Normand put through his own net in the 18th minute.
It was the eighth own goal scored at this year's competition and the first time Spain had conceded at all after they registered three clean sheets during the group phase.
However, Spain had beaten Willy Sagnol's Georgia side twice in qualifying, winning 7-1 away and 3-1 at home, and their class ultimately told on a rainy night.
Rodri Hernandez stroked in the equalizer six minutes before half-time, and Fabian Ruiz headed in a Lamine Yamal cross to put Spain ahead on 51 minutes.
Khvicha Kvaratskhelia had come close to scoring from inside his own half for Georgia just before that, but Ruiz's goal effectively ended their hopes of causing a monumental upset.
Nico Williams ran from halfway to score a brilliant third goal for Spain on 75 minutes and substitute Dani Olmo wrapped up their victory seven minutes from time.
Luis de la Fuente's team, who missed a host of chances to win by a greater margin, will now go to Stuttgart for a clash with the host nation on Friday.
That game is also a repeat of the Euro 2008 final which Spain won 1-0 to begin their golden era.
"We're very happy because we know what it takes to be here. That's been shown by what the other teams have gone through," De la Fuente told Spanish television.
"(The result) was deceptive because it could have been 8-1 or 9-1. We had to suffer, counter-attacking is their weapon."
Georgia go home with their heads held high after a memorable first appearance at a major tournament which saw them defeat Cristiano Ronaldo's Portugal to reach the knockout phase.
"I am very proud of what the players have done in the last months," Frenchman Sagnol said.
"Now it is the end of the journey but I am sure the next one will also be very exciting."
The last-16 action continues on Monday as Kylian Mbappe and France take on Belgium in Duesseldorf at 1600 GMT before Portugal meet Slovenia in Frankfurt in the late game.