Sevilla, who won the Europa League for the seventh time last season, took the lead in the 25th minute of the contest through Youssef En-Nesyri.
Cole Palmer levelled the scores in the 63rd minute of the contest, though, and that was how it finished in normal time, with penalties needed to decide the winner.
Erling Haaland, who found it difficult to make his mark in normal time, scored in the shootout alongside teammates Julian Alvarez, Mateo Kovacic, Jack Grealish and Kyle Walker.
Sevilla were successful with their first four penalties, with Lucas Ocampos, Rafa Mir, Ivan Rakitic and Gonzalo Montiel on the scoresheet, but Nemanja Gudelj missed the vital spot kick at 5-4 to allow Pep Guardiola's side to secure the trophy on penalties.
More to follow.