Juventus eliminated FC Porto in Tuesday's other game thanks to a 1-0 win in the second leg, completing a 3-0 aggregate victory.
It was a sorry night for Sevilla and its frustrated coach Jorge Sampaoli, who was sent to the stands in the closing stages for complaining to the match officials. The Spanish side was looking to qualify for the Champions League quarterfinals for the first time but couldn't match the intensity of the home side.
As for Leicester, life just gets better in its first season in Europe's top club competition. This was its third straight win since last season's title-winning coach Claudio Ranieri was fired, with the team fighting a relegation battle in its Premier League title defense.
Craig Shakespeare is Leicester's new coach and he has the chance to orchestrate another miracle.
This was Shakespeare's first game since he was hired as manager until the end of the season on Sunday, and Leicester marked the occasion - possibly its highest-profile match ever - by unfurling a huge banner at one end of the stadium before kickoff with a picture of the coach holding a dog on a leash above the words "Let slip the dogs of war." It was a line from 'Julius Caesar,' a play by William Shakespeare.
Across the field, banners with the words "Forever" and "Fearless" hung from the stadium roof, as blue-and-white fluttered around.
It made for an electric atmosphere, the kind that carried Leicester to its improbable title triumph last season. While it seemed to get to Sevilla's players, it inspired the home side.
Leicester was quicker to most balls, playing a simple but highly effective game. Morgan's goal typified that.
After Vardy was tripped at the corner of the area, Mahrez swung over a left-footed free kick and Morgan stuck out a foot at the far post to divert the ball into the net and become the first Jamaican to score in the Champions League.
Sampaoli snarled and raged in his technical area and was clearly unhappy at halftime because his players were sent out early for the second half, with two substitutions made.
The match was still very much in the balance, with Leicester just one conceded goal away from going out and that almost happened when Sergio Escudero drove a dipping 35-meter shot against the crossbar.
A minute later, Albrighton was sending the King Power into raptures when he drove a low shot into the corner after Mahrez's cross was poorly cleared by Adil Rami.
Sevilla dominated the final 30 minutes but its task was made harder when Nasri, who was booked in the first half for a petulant swipe at Wilfried Ndidi's ankles, collected another yellow card for going head to head with Vardy and aiming a butt.
There was still time, though, for N'Zonzi to stroke a weak penalty at Schmeichel - diving to his left - as the night finished dramatically.
