Diego Carlos made amends for conceding a penalty earlier in the final with a 74th-minute overhead kick that went in via Romelu Lukaku's right foot. Antonio Conte called Alexis Sanchez, Christian Eriksen, and Victor Moses off the bench to try to turn the game back in Inter's favor, but they were unable to breach Sevilla for a third time.
Julen Lopetegui and some of his Sevilla players were in tears when the final whistle sounded.
Inter took the lead after Carlos surrendered his third penalty in as many games. The Brazilian, who was one of La Liga's standout center-backs before his recent errors on continental duty, dragged Lukaku to the ground to concede a spot-kick and picked up a yellow card, despite a gang of Inter players demanding harsher punishment for Carlos. Lukaku converted from the spot in the fifth minute, extending his Europa League scoring streak to 11 matches.
Luuk de Jong responded soon after. Sevilla built patiently before Jesus Navas was found in space wide on the right. His delivery was whipped into the area, where De Jong's stooping header turned it in. The pair combined again after Navas assisted De Jong's winner in the semifinal against Manchester United.
The match was hotly contested, with referee Danny Makkelie facing incessant complaints when flops and flailing arms punctuated attacks. Inter boss Antonio Conte received a yellow card after expressing his displeasure at not being awarded another penalty, this time for an apparent handball.
Then, in the space of 134 seconds, it was 2-2 - and both goals were quite similar. The first came from Sevilla when De Jong met Ever Banega's set-piece with a header that looped over a helpless Samir Handanovic. Inter's second tally was another set-piece swung toward the back post, where it was sent into the net by an emphatic Diego Godin header.
The first half was a tough act to follow. Yassine "Bono" Bounou rushed off his line to thwart Lukaku in a one-on-one situation and Sevilla fashioned a few promising moves, but the second stanza couldn't match the breakneck speed of its predecessor. Plenty of players felt the strain: Sevilla's star Lucas Ocampos, who was withdrawn during the semifinal due to injury, was replaced by Munir El Haddadi in the 71st minute.
But the final still had another trick up its sleeve, with Carlos and Lukaku involved once more. Sevilla lifted another set-piece into the Inter area and, when an attempted clearance spiraled into the air, Carlos took up the invitation. The former Nantes man turned around and flicked his body backward to execute an excellent overhead kick. He was awarded the goal despite Lukaku helping the ball on its way into Handanovic's net.
Conte introduced some substitutes and instructed his team to attack. But Jules Kounde's goal-line clearance and some disciplined defensive work from Sevilla kept the Nerazzurri at bay.
Lopetegui was tasked with reconstructing Sevilla as sporting director Monchi brought 14 new players aboard last summer, but he has impressively molded a side capable of winning Europe's secondary competition and competing in the Champions League next season.
It was the emotional Lopetegui's first club honor in a coaching career that appeared doomed following last term's disastrous, short-lived spell at Real Madrid.