Jurgen Klopp was left lamenting yet another final reverse as the Madrid-born midfielder put the Reds to the sword after the interval, with Gameiro also on target
Two goals from Coke saw Sevilla come from behind to win a third consecutive Europa League with a 3-1 victory over Liverpool in Basel.
Unai Emery's men, outplayed in the first half, responded with an emphatic second 45 minutes to leave Liverpool reeling and condemn Jurgen Klopp to a fifth straight defeat in a major final.
Liverpool, which had dispatched Villarreal so impressively in the second leg of the semifinal, was the better side in the first half and deservedly took the lead when Daniel Sturridge curled in a superb finish from the edge of the area.