Carlos Bacca claimed the plaudits with a superb double strike, including a late winner to decide a pulsating clash that began at a hair-raising pace with four goals in the first half.
It was an energetic end-to-end battle for most of the match.
Dnipro had grabbed an early lead from Nikola Kalinic before Sevilla hit back with goals by Grzegorz Krychowiak and Bacca.
A free kick from Dnipro captain Ruslan Rotan made it 2-2 just before the break and it looked like the Ukrainians, playing in their first European final, might cause a stunning upset.
But Bacca settled the game for Sevilla and secured the trophy and a precious Champions League place handed to the winners for the first time as they go into the group stage.
Colombia striker Bacca, substituted before the end, broke down on the bench with the emotion of it all as the final whistle sounded and the celebrations began.
Sevilla are now the undisputed kings of the competition, having also won it twice in its former guise as the UEFA Cup in 2006 and 2007, and have moved ahead of Juventus, Liverpool and Inter Milan to stand alone with most wins on the honours board.
FIRST BLOW
Predictions that this would be a cagey affair were swiftly confounded as the teams tore into each from the start.
Within minutes of the kickoff Dnipro landed the first blow.
A chip forward found Kalinic and he nodded the ball deftly into the path of Brazilian winger Matheus, whose precise cross was met by the Croatia target man to head low into the net past the sprawling dive of Sevilla keeper Sergio Rico.
That seemed to spark some life into the wounded Spaniards and Krychowiak levelled after 28 minutes.
The Poland international raised the roof off the stadium in his home country when he received Bacca's knockdown, took a touch to get the ball out of his feet and drove his finish through several Dnipro bodies into the net.
Within three minutes Sevilla were ahead as Reyes set Bacca clear with a perfectly weighted through ball and the Colombian rounded keeper Denys Boyko before calmly slotting home.
That could have proved a devastating psychological blow to Dnipro, but the rugged Ukrainians are made of stern stuff and they equalised before the break through Rotan's superb curling freekick that looped delicately over the wall and into the net.
The second half was a much nervier affair, before Sevilla struck the decisive blow. Vitolo's flicked pass found Bacca who stayed onside to turn in the area and drill the ball home.
(Editing by Ken Ferris)
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