The Ukrainians had fought back to earn a 1-1 draw in the first leg of their semi-final and they grabbed the only goal of the return meeting to earn a 2-1 win that has booked their first ever appearance in a European final.
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The Argentine had another decent opening for the visitors after he was picked out by Faouzi Ghoulam's cross, but his header was tipped behind by the keeper.
As the game moved past the half-hour mark, Dnipro came close to finding the net when Yevhen Seleznyov's curling strike was touched behind by the fingertips of Andujar.
The hosts created another promising opportunity at the start of the second half, as Valerii Luchkevich was picked out by Seleznyov, before dragging a shot wide of the far post.
Dnipro were showing far more attacking intent than their opponents and Seleznyov caused another moment of danger with a low curling strike into the gloves of the keeper.
The Ukrainians then stunned their opponents in the 58th minute by taking the lead, as Seleznyov made the most of some poor defending to head Konoplyanka's cross into the top corner.
However, the Ukrainians continued to pose a danger on the break and Nikola Kalinic's powerful drive was beaten away by Andujar, before the keeper was up quickly to save his follow-up.
The hosts then came within inches of making the game safe as Matheus looped a header over Andujar, but the ball came crashing back off the crossbar.
Dnipro's missed chances would not come back to haunt them, though, as they withstood heavy pressure from Napoli to see out the match and set up a final against holders Sevilla.