Goalkeeper Kasper Schmeichel saved a late penalty to help the defending Premier League champions beat Sevilla 2-0 in the second leg and win the match 3-2 on aggregate.
Trailing 2-1 from the first leg, Leicester opened the scoring through Wes Morgan in the first half.
Marc Albrighton increased the home side’s lead with a goal in the second half that gave them a 3-2 lead on aggregate.
Sevilla, winners of the last three Europa Leagues, could have forced the tie into extra time after they were awarded a penalty kick in the 81st minute. However, Schmeichel denied Steven N’zozi’s effort with a save low to his left.
The win carries on a remarkable turnaround under new manager Craig Shakespeare, who has won three games in a row since replacing Claudio Ranieri, who was sacked after the first leg loss to Sevilla three weeks ago.
“I think we have to play to our strengths,” Shakespeare remarked after the match.
You saw that in abundance in the performance (against Sevilla), in terms of desire, but we can play a bit as well. Beating Sevilla epitomises what we’re about,” he said.
In Tuesday’s other round-of-16 second leg tie, Juventus eased into the last eight with a clinical performance against Porto in Turin.
Paulo Dybala struck from the penalty spot as the Italian champions beat Porto 1-0 on to complete a 3-0 aggregate victory.
Porto’s hopes of overturning the 2-0 deficit were extinguished when Maxi Pereira was sent off for handball in the 41st minute.
Argentine striker Dybala duly converted the resulting penalty to give Juventus a quarterfinal berth.
The quarterfinal draw takes place on Friday.