Trailing 2-1 from the first leg, the reigning Premier League champions went ahead at the King Power Stadium through Wes Morgan’s close-range finish.
Marc Albrighton then gave the Foxes an aggregate lead before Samir Nasri was sent off for a second yellow card.
Steven N’Zonzi missed a penalty as Sevilla tried to take it to extra time.
The Foxes join Barcelona, Bayern Munich, Borussia Dortmund, Juventus and Real Madrid in reaching the last eight.
Who was your man of match?