It was all Sevilla in the first period as the Foxes spent the majority of the half on the ropes, with a penalty miss from Joaquin Correa and chances for Sergio Escudero and Stevan Jovetic.
However it was a 25th-minute effort from Pablo Sarabia that separated the sides at the break.
The second period lack the same intensity but certainly didn't lack in drama, with a good chance from Vitolo before Correa looked to have secured the tie just after the hour mark.
The Foxes were beginning to come into the game and a strike from Vardy gave them some hope, another chance for Vitolo and Adil Rami followed but the Foxes held out to set up a interesting return tie at the King Power Stadium on March 14.
Soaking up the pressure
Claudio Ranieri's side weren't given much chance entering Ramón Sánchez Pizjuán Stadium considering their recent form, and they were certainly under the quash from the first whistle.
The game was barely ten minutes when the Foxes jangled their own nerves, as Christian Fuchs' header backwards forced Kasper Schmeichel into what would be the first of many saves on the night.
It looked like that Jorge Sampaoli's side were going to be handed the lead when they were awarded a penalty, Correa did well to get the ball ahead of Wes Morgan who produced a reckless challenge.
Clement Turpin made the easy decision of pointing to the spot, Correa stepped up but he fluffed his lines as his penalty was easily saved by Schmeichel down the middle.
Schmeichel looked to be in for a long night as he was called up again in the 22nd minute, Escudero was found on the edge of the area and hit a sweet shot but Schmeichel was there to keep it from creeping in.
Taking a deserved lead
However, there was nothing the Dane could do from prevent their Spanish opponents from taking the lead moments later, and deservedly so as it was a brilliantly worked goal from the Spaniards.
Escudero produced a great ball which curled away from the back post, Fuchs looked to have covered but Sarabia rose brilliantly to power a header back across and into the far corner to send the crowd into a frenzy.
The onslaught failed to give way as Jovetic had an excellent chance for two moments later, he tried one from some distance but it was deflection from Robert Huth which forced Schmeichel to tip it behind.
Correa then had a good opportunity in the 37th minute, but his shot from 20 yards out was well tipped away by the impressive Schmeichel.
Keeping up the pressure
The Spaniards didn't let up as the second period got underway, and had a great chance just six minutes after the restart. Samir Nasri produced a great ball taking five Leicester players out the game and sent Vitolo through, the angle was against him but he whiskers away from the second as the effort skimmed the post.
It was only ten minutes later that they managed to double their lead, and it was an act of redemption from Correa. It was poor from Leicester as Jovetic broke down the middle and had Huth and Morgan in knots, he produced a great turn before laying it to Correa who smashed it into the roof of the net.
Getting one back
Ranieri's side had hardly been the game in a attacking sense, but were beginning to look dangerous as the half went on and they were rewarded with a vital away goal in the 73rd minute.
It was textbook as Danny Drinkwater broke down the left touchline, he laid it on a plate for Vardy who was waiting to fire home from eight yards out to tap home his first goal Champions League goal and first of 2017.
All the Foxes had to do from that point was hold out, but it wasn't made easy for them by Sevilla. Sarabia's deflected ball in the 83rd minute looked good for Vitolo, but once again Schmeichel was there to block it.
There best chance came in the final minute of normal time, when Rami rose highest to the corner in but it flicked off the crossbar.