Geronimo Rulli saved a spot-kick from his fellow goalkeeper David De Gea for what was the 22nd attempt of a thrilling yet incredibly tense shootout. The two teams played out a dreary 1-1 draw over the preceding 120 minutes.
The victory secured Villarreal's first major trophy in their 98-year history. It was also the fourth triumph in five Europa League finals for manager Unai Emery, who only fell short in the competition's showpiece during his ill-fated spell in charge of Arsenal.
Ole Gunnar Solskjaer, who missed out on the first trophy of his United reign, selected a positive lineup, and his team was in charge from the start. However, Villarreal took the lead against the run of play through their prolific frontman Gerard Moreno.
United's backline positioned itself high up the pitch for Dani Parejo's set-piece and couldn't react quickly enough when the playmaker floated his delivery toward the penalty spot. Victor Lindelof desperately tried to scramble back but couldn't stop Moreno from jabbing the ball past De Gea.
Parity was restored through Edinson Cavani. Marcus Rashford smashed the ball back into the area after Villarreal nodded away a United corner, and the Uruguayan striker tapped in from eight yards following some pinball in the area.
The most intriguing aspect of the final thereafter was Solskjaer's reluctance to make substitutions - he didn't make one until the 100th minute and then hurried a further four changes with four minutes of extra time remaining. Solskjaer's mind, it seemed, was on the upcoming penalties.
And the spot-kicks that followed were of the highest quality. Opposing players took turns in successfully converting from 12 yards until the spectators in Gdansk were treated to the rare spectacle of goalkeepers taking the 21st and 22nd penalties in a shootout.
Rulli confidently smashed his effort into the top corner before pushing De Gea's shot away down to his left, prompting jubilant celebrations from the Europa League final underdogs.