Inter was the favorite coming into Friday's final, played behind closed doors in Cologne, Germany, and Sevilla certainly earned its win the hard way.
Romelu Lukaku, who has found a welcoming home at Inter following a mixed stay at Manchester United, gave his side the lead from the penalty spot inside five minutes.
Sevilla fought back and two first-half goals from Luuk De Jong looked to have swung the final in its favor, but Inter equalized through Diego Godin just two minutes later.
Just when it looked as though Inter was on the brink of finding a winner, defender Diego Carlos acrobatically gave Sevilla the lead late on, thanks to a large deflection off Lukaku's outstretched boot.
It was a performance of grit and determination, interspersed with some brilliant attacking football, that Sevilla had to fight tooth and nail for from the opening whistle.
Dutch referee Danny Makkelie was officiating in his first major European final and to say that the opening 20 minutes were a baptism of fire would be something of an understatement.
Every foul, even the most obvious, drew a swarm of opposition players around him, vehemently protesting his decisions. Any fears that this final would lack intensity due to the empty stands were quickly dispelled.
The small delegation of Sevilla officials, all dressed smartly in suits, were making a fine effort of replicating the missing atmosphere in the vacant stands of the 50,000 capacity RheinEnergieStadion.
Makkelie would have a huge decision to make inside five minutes after Carlos clumsily hauled Lukaku to the ground inside the penalty area.
The referee correctly pointed to the spot to give Carlos a sense of déjà vu -- the Brazilian had conceded penalties in the quarterfinal, semifinal and now the final. Carlos protested his innocence but, in truth, he was fortunate not to be shown a red card as well.
Lukaku stepped up and calmly placed the penalty past goalkeeper Yassine Bounou for his 34th goal of the season, matching the record set by the great Ronaldo Nazario in 1997-98 as the player with the most goals in his debut season at Inter.
Inter thought it should have been awarded a second penalty soon afterward but the officials waved away their appeals, resulting in head coach Antonio Conte being booked for his furious protests.
But Sevilla are the undisputed kings of this competition. The Spanish side has now won the title a record six times, with all of those victories coming in the past 15 years, and there is just something about this trophy that spurs the club to greater heights.
And in the space of 20 minutes, Sevilla had turned the game on its head. Two stunning headers from de Jong -- the first a brilliant stooping effort and the second at the far post -- gave Sevilla the lead.
Sevilla coach Julen Lopetegui has found redemption at the Andalusian club. The 53-year-old drew the ire of the Spanish Football Federation -- and much of Spain -- when he agreed to become manager of Real Madrid just days before the start of the 2018 World Cup.
He was sacked just two months after his first official game in charge and made the fall guy for the club's poor performances. It would be the best part of a year before he was offered another job, but Sevilla welcomed Lopetegui with open arms and he has more he repaid the faith shown in him.
After guiding the club to fourth in La Liga, he was now less than an hour away from delivering a major European trophy.
But Conte has similarly changed Inter's fortunes in his first season in charge.
The Italian club has a rich and storied history, but has long been considered one of European football's sleeping giants. It won an unprecedented treble as recently as 2010, but success since then has been hard to come by.
After relentless success in in the early 2000s, the club has become one of many in Italian football that have struggled over the last 10 years. However, Conte is a serial winner and guided Inter to the brink of a first major trophy since 2011.
The passion with which he coaches his team from the technical area also oozes through his players and it was his captain Diego Godin that drew the sides level less than three minutes later, powering home a header at the far post.
After a whirlwind opening half, the two teams showed no signs of slowing down in the second period and Sevilla goalkeeper Bounou pulled off two sharp saves to keep his side level.
But in a dramatic twist of fate that was befitting of this thrilling final, Diego Carlos, the man who perhaps should have been sent off in the opening five minutes, popped up in the penalty area and fired a bicycle kick at goal.
His initial effort might have been going wide, but Lukaku reflexively stuck out a boot and directed the ball into the roof of the net. The kings of the Europa League were once again on the brink of glory.
Sevilla needed some heroic defending to preserve its slender advantage. Carlos, Jules Koundé and Sergio Reguilón threw their bodies in the way to deny substitutes Victor Moses and Alexis Sánchez.
At the final whistle, Sevilla's players collapsed to the turf, many through sheer exhaustion and others sobbing with joy at their achievement.
Some of them, like veterans Éver Banega and Jesús Navas, have won this competition multiple times, but the club underwent a huge rebuilding process last summer. For most of these players, this was a first major European trophy -- it was a first trophy as manager for Lopetegui, too.
Sevilla has now reached the Europa League final six times and won it on every occasion. There's something in the air in Andalusia.