Trailing 2-1 from the first leg, after which Claudio Ranieri was sacked as manager, Leicester scored through Wes Morgan and Marc Albrighton before Schmeichel repelled Steven N’Zonzi’s spot-kick.
It gave them a 3-2 aggregate win and continued a remarkable turnaround under new manager Craig Shakespeare, who has won three games in a row since stepping up from his role as Ranieri’s assistant.
They also chose a good time to rediscover a bit of defensive solidity — and good fortune — having previously gone 12 matches without keeping a clean sheet in all competitions.
Sevilla, winners of the last three Europa Leagues, saw Samir Nasri sent off late on after he was shown an extraordinary second yellow card for aiming a headbutt at Jamie Vardy.
N’Zonzi might yet have taken the game to extra time after Schmeichel was penalised for catching Vitolo after the forward had dinked a shot past him. But the Dane redeemed himself with a save low to his left, thwarting Sevilla’s hopes of reaching the last eight for the first time since 1958.
The back-to-back 3-1 wins against Liverpool and Hull City overseen by Shakespeare had restored Leicester’s self-belief and the stadium crackled with anticipation prior to kick-off.
A carpet of blue and white flags greeted the teams, while Leicester’s fans unveiled a giant banner of Shakespeare, accompanied by the rousing William Shakespeare quote: “Let slip the dogs of war.”
For all the sound and fury generated by the home support, it was Sevilla who procured the first two sights of goal.
– Escudero missile –
Nasri, one of eight changes made by Jorge Sampaoli, was denied by a one-handed save from Schmeichel in the fourth minute, while Pablo Sarabia dragged wide with his left foot.
But in the 27th minute Leicester took control of the tie, Riyad Mahrez swinging a free-kick into the box after Vicente Iborra had felled Vardy and Morgan bundling home with his right knee.
The King Power Stadium erupted with a noise that recalled the triumphs of last year and short of a mishit Gabriel Mercado cross that Schmeichel had to palm over, Leicester reached the break without alarm.
Sampaoli made two changes at half-time, sending on Mariano Ferreira and Stevan Jovetic for Mercado and Sarabia, and eight minutes in his side came within millimetres of restoring their advantage.
Sergio Escudero let fly with a fluttering effort from 35 yards that crashed against the bar before bouncing down and out, with Jovetic hoisting the rebound over. Barely a minute later Leicester took the lead in the tie outright.
Mahrez’s cross from the right was tamely headed away by Adil Rami, allowing Albrighton to chest the ball down and arrow a left-foot drive past a statuesque Sergio Rico. Nasri’s moment of madness arrived shortly after Schmeichel had parried from substitute Joaquin Correa.
With play ongoing, the Frenchman, taking exception to a push from Vardy, squared up to the England striker and lowered his head, prompting a second yellow card from referee Daniele Orsato.
Orsato was not prepared to abandon centre-stage and after awarding Sevilla’s penalty, he compounded the visitors’ frustrations by sending the protesting Sampaoli to the stands.