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Antonio Conte's free-scoring Inter side got the openerat theRheinEnergieStadion, with Romelu Lukaku netting his 34th goal of the season from the penalty spot with only five minutes on the clock.
However, Luuk de Jong headed home a pinpoint Jesus Navas cross to levelthe scorejust seven minutes later, and he repeated the trick just after the half-hour mark.
Inter then scored an equaliser of their own through Diego Godin, before both teams managed to compose themselves defensively while looking for a winner.
The all-important final breakthrough came late in the second half, when Lukaku put through his own net in unfortunate fashion after sticking out a leg to try and block a Diego Carlos overhead kick.
Sevilla held on for a famous 3-2 victory, and Lopetegui paid tribute to two-goal hero De Jong and the rest of his squad for their never-say-die attitude.
"It is very special. Always it is very special to win a cup," the 53-year-old told reporters. "For us, for me, for the fans, it is very special. We have a happy ending.
"Luuk de Jong is a very good player, he worked for his moment and he was ready in the right moment.
"We had three penalties in the last three matches in the first five minutes but our team never surrenders."
Lopetegui went on to comment on the imminent departure of Ever Banega, who will soon undertake a new challenge inSaudi Arabia after three successful years with Sevilla.
The Spanish coach said of the Argentine's decision to leave the club: "I am not surprised. I am sad he is leavingbut I am not surprised. He is a fantastic player with a good mentality."
De Jong says that Loopetegui told him he was starting the final at the eleventh hour, and he was glad to repay his manager's faith on the biggest stage.
"It is incredible. We had such tough games all tournament but we played so well as a team," the Dutchman told BT Sport.
"We were like a family, we worked together. It didn't matter who came in. It was tough. We started well but they scored out of nothing. Two goals, amazing feeling for me.
"The manager told me this morning I was starting. I told him I am always ready when he needs me and today it worked really well."