Goals from Wes Morgan and Marc Albrighton turned the tie on its head but the Foxes were equally indebted to Kasper Schmeichel, who denied the ten-man visitors from the spot.
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Leicester City's remarkable UEFA Champions League debut surges on after the English title holders ousted a Sevilla side that have won European silverware for the past three seasons to reach the last eight.
Trailing 2-1 from the round of 16 first leg, Leicester reversed their fortunes with goals from Wes Morgan and Marc Albrighton but there was plenty more drama to come. First Samir Nasri was sent off, then the ten men won a penalty. However, Kasper Schmeichel, who had denied Joaquín Correa from the spot in Seville, repeated the feat against Steven N'Zonzi as the Foxes held on.
The visitors had been on top when Morgan inadvertently bundled the ball in midway through the first half. If there was an element of luck about the first, not so the second as Albrighton coolly slotted in from the edge of the box.
That said, moments before the goal that made it 2-0 on the night, Sergio Escudero struck the underside of the bar at the other end with a stunning long-range effort, and even Nasri's dismissal did not end Sevilla's challenge. Schmeichel saw to that.
Key player: Kasper Schmeichel
It is no revelation that Schmeichel is made of the 'right stuff' in UEFA Champions League terms. After all, he has lineage (father Peter, take a bow). However, it is one thing to be an exceptional footballer and quite another to show it precisely when you need to most. Sure, there was the penalty save but equally important was his intervention to keep out Nasri's ferocious early shot. That could have been the killer blow – not on Schmeichel's watch.
Leicester seize the day
To put Leicester's triumph into context, this was their first victory in a two-legged European tie since 1961. This group of players played like they knew this was a once-in-a-lifetime opportunity. So too the home supporters who created a wonderful atmosphere, getting right behind the team from the moment a giant flag of new boss Craig Shakespeare was unveiled with the accompanying message: "Let slip the dogs of war." Sevilla certainly felt their bite.
Sevilla fall for Foxes' trap
No club in the Liga play like Leicester and few around Europe have their mix of power, pace and robust strategy. Sevilla couldn't cope. Little by little they were suckered into precisely the kind of speed and strength-based contest in which the English champions are experts. Elimination, and seeing history slip away from them, is painful enough. But to depart without showing their true footballing personality, that's a soreness that will take time to dissipate.
Simon Hart, Leicester (@UEFAcomSimonH)
"Champions of England we know what we are." The Leicester fans may sing it but there have been times this season when their side have looked anything but. This was different – it was last year's template replicated to perfection. It showcased everything good about this team in a performance of tremendous intensity, desire and togetherness. They pressed Sevilla tirelessly. And when it mattered they produced the clinical touches in front of goal – plus decisive saves by Schmeichel – to earn their biggest victory on the continental stage.
Graham Hunter, Sevilla (@BumperGraham)
Playing three at the back meant that, with Vardy left to forage on his own, Sevilla had one too many men in the defensive set-up and one too few higher up the park. It took until nearly half-time for the side to recalibrate. By then, though, the damage had been done and the English title holders, with their blood already up, needed no second invitation. With hindsight, would Stevan Jovetić, provider of four goals and four assists in 12 games, have had a greater impact if deployed from the off rather than the interval?