Dnipro, appearing in their first ever European final, took and then squandered a lead before levelling up late in the half to go in at 2-2 against last season's champions.
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The holders had the first sight of goal inside the opening minutes when the ball fell to Carlos Bacca in space on the edge of the penalty area, but he sliced his half-volley well off target.
Jose Antonio Reyes, playing what may be his final game for the club, was then denied a penalty claim by referee Martin Atkinson, and things went from bad to worse for the Spanish side as they soon found themselves behind.
Having soaked up the early pressure, Dnipro hit Sevilla on the break, with Nikola Kalinic flicking the ball on to Matheus Nascimento and immediately looking to get into the box for the return. Matheus duly found him with a cross hung up into the middle, and Kalinic made no mistake when nodding the ball past Sergio Rico.
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Unai Emery's side found themselves with the task of breaking down a Dnipro team who have more clean sheets in this season's competition than anyone else, and they had a chance to do so when Benoit Tremoulinas set up an opening for Vitolo. However, the midfielder opted against taking the shot first time and eventually saw his effort blocked.
Sevilla continued to see most of the ball and came close again when Reyes cut inside before flashing a powerful low effort narrowly past the near post.
The team who have scored first in the final of this competition have not failed to win the trophy since 2004-05, but Dnipro needed goalkeeper Denis Boyko to be alert when he tipped Grzegorz Krychowiak's free header round the post following a corner.
A rare defensive lapse saw Dnipro switch off from a free kick to almost let Reyes in, but from the resulting corner they were punished. A loose ball dropped to Krychowiak in the box and he kept his composure before drilling a shot low past Boyko.
The turnaround was complete with a second goal in the space of three minutes as Reyes threaded a pinpoint through-ball forward to Bacca, who took it around a helpless Boyko before rolling it into an empty net to turn the final on its head.
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Suddenly it was Dnipro who needed to get onto the front foot, and Yevhen Konoplyanka attempted to restore parity with a vicious curling effort towards the top corner that Rico managed to flick over the bar with a flying stop.
At the other end, Boyko could only watch on as a thunderous Aleix Vidal strike sailed towards the top corner, only for the ball to rise inches over the bar.
It was Dnipro who would get the game's fourth goal, however, and it was another long-range effort that made the difference as Ruslan Rotan clipped a free kick over the wall and beyond the despairing dive of Rico with just a minute of the half remaining.
The last European final to see four first-half goals came in the UEFA Cup back in 2001, when Liverpool went on to beat Deportivo Alaves 5-4 after extra time.