The Spanish side had to come back from a goal down as Nikola Kalinic headed Ukrainians Dnipro into an early lead.
Sevilla responded with two quick goals as Grzegorz Krychowiak drove in before Carlos Bacca rounded the goalkeeper.
Ruslan Rotan's clever free-kick made it 2-2, but Bacca broke through to seal victory for Sevilla and with it a place in next season's Champions League.
Unai Emery's side are the first to successfully retain the trophy and have now won the Europa League/Uefa Cup more than any other team, having triumphed in 2006, 2007 and 2014.
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