Meanwhile in the Europa League, Manchester United progressed to the last 16 with a win in France
At more than one stage tonight did it feel as though Leicester City would be on the receiving end of a Sevilla rout, but Jamie Vardy's second half strike has given them a fighting chance when the La Liga side visit the King Power Stadium in three weeks time.
The scoreline at the Estadio Ramón Sánchez Pizjuán read 2-1 as the final whistle went, but Claudio Ranieri will know the damage could have been a lot worse.
By the time Jorge Sampaoli's side visit Leicester in March, the Premier League champions could be sucked even further into a relegation battle and another night in Europe could prove unwanted, but after tonight's performance their European Odyssey lives on.
They had Kasper Schmeichel to thank when they conceded a penalty in the opening 13 minutes of the game. The Dane was on hand to deny Joaquin Correa from the spot.
Their resistance wasn't to last when Sergio Escudero whipped a cross into the back post. Christian Fuchs, who almost was at fault for an own goal in the opening stages, was caught sleeping and Pablo Sarabia was on hand to head past Schmeichel.
Leicester were made to withstand pressure up until the break, Correa again going close but kept out thanks to a good stop from the Leicester netminder.
Pablo Sarabia with his teammates celebrates scoring the opening goal of the game in their Champions League Round of 16 first leg tie. Image: Miguel Morenatti AP/Press Association Images
After the break, Sevilla pressed on with more of the same. After hitting the post in the opening 10 minutes of the half, they doubled their lead just after the hour mark.
Correa was on hand to capitalise on Robert Huth and Wes Morgan's mistake in the Leicester defence. Stefan Jovetic fed his fellow striker and he finished high into the net to all but secure the victory got Sevilla.
But of course, as has been the case with Leicester over the last three years, they just didn't know when to quit.
Sevilla didn't know quite what to do, then, when Danny Drinkwater - a towering figure for them last season but anonymous since the start of the new term - began driving at the defence.
He made his way down the left and squared a low driven cross toward Vardy who was on target for his first ever European goal.
Late chances from Sevilla were spurned and Leicester were able to hold out and carry a priceless away goal into the second leg.
Juventus also have one foot in the Champions League quarter-finals with a 2-0 win away to 10-man Porto this evening.
Alex Telles was dismissed before the hour mark after picking up two bookings in two minutes. The Italian giants then punished their Portuguese counterparts with two goals in two minutes from Marko Pjaca and Daniel Alves.
Jamie Vardy on target to throw Leicester City a lifeline against Sevilla in the Champions League. Image: Miguel Morenatti AP/Press Association Images
Elsewhere tonight, Manchester United booked their place in the last 16 of the Europa League with a 1-0 win away to Saint-Étienne in France.
Jose Mourinho's side carried a 3-0 aggregate lead into the game before Henrikh Mkhitaryan popped up in the first half to get on the end of Juan Mata's cross. His poked effort was enough to go past Stephane Ruffier for the only goal of the game.
There was some concern for the Armenian when he was substituted on 25 minutes. Clutching his thigh, he left the pitch to be replaced by Marcus Rashford who was his usual energetic self.
It didn't go all United's way this evening. Defender Eric Bailly was dismissed in the second half for picking up two yellow cards.
Meanwhile, Schalke 04 drew 1-1 with Greek side PAOK but progressed through on an aggregate scoreline of 4-1. United's group stage opponents Fenerbahçe were knocked out of the competition by drawing 1-1 with FC Krasnodar, losing 2-1 on aggregate.