After an unspectacular match ended 1-1 after extra time, Sevilla ruthlessly punished the Italians in the shootout, with Gonzalo Montiel firing home the winning spot kick, just as he did for Argentina in the World Cup final against France.
The defender had missed his first effort but was handed a reprieve when Roma keeper Rui Patricio was adjudged to have come off the line too early and he made no mistake with his second, sparking jubilant celebrations.
Sevilla keeper Yassine Bounou was their hero in the shootout, saving penalties from Gianluca Mancini and Roger Ibanez while the Spaniards were flawless in their own execution, scoring their first four.
Sevilla, the undisputed kings of the Europa League, have now won all seven of the finals they have played in the competition, and are well-versed in the drama of the occasion, having seen their opponents score first in the last four finals.
It was a tense and ill-tempered affair from the start on Wednesday, with Roma defending deep with a five-man backline against Sevilla, who had almost 65% possession but were kept mostly outside the Italian's crowded box.
The match was tetchy with referee Anthony Taylor dishing out 14 yellow cards, the most ever in a Europa League game, and playing almost 30 minutes of stoppage time in total.
Paulo Dybala gave Roma the lead from a counter-attack in the 35th minute but Sevilla then took control of the game and found the equaliser thanks to an own-goal by Mancini in the 55th minute.
Sevilla dominated the match after that but Roma had the better chances from counter-attacks and set-pieces, including a Chris Smalling header that hit the crossbar in the 10th minute of added time in extra time.
Sevilla maintained their incredible record in the competition after an otherwise difficult season.
Languishing in the bottom half of LaLiga for a large part of a campaign in which they fired two managers, Sevilla only rediscovered their form after exiting the Champions League.
Their run to the final saw them beat PSV Eindhoven, Fenerbahce and Manchester United before downing Juventus in the semis.
"It was a Sevilla-style match. We have to suffer to win," Lucas Ocampos told Spanish TV channel Movistar Plus.
"This is not easy. What we have with this competition is something that cannot be explained."
It was the third consecutive Europa League final that ended in a penalty shootout.
The win means Sevilla will compete in next season's Champions League despite finishing outside the top four in the LaLiga.
Mourinho had never lost a European final before Wednesday, having last year led Roma to the inaugural Europa Conference League title, becoming the first coach to win all the European trophies.
Losing was clearly a painful experience for the Portuguese who handed his runners-up medal to a fan in the stand after the presentation.
"That's what I did, I don't want silver medals. I don't keep silver medals, so I gave it away," he told Movistar.