Victor Nilsson Lindelöf became the last penalty taker of the outfielders.
He put 10-10 after Villarreal's goalkeeper Gerónimo Rulli was on the ball with his fingertips.
By then, all 20 outfielders had put their penalties in a perfect display.
Then Rulli himself put 11-10 for Villarreal and then went and stood in the goal and saved David De Gea's penalty by throwing himself into the left corner and parry out the ball.
With five minutes left in extra time, a hand was examined in United's penalty area after the ball landed on Fred's arm but the referee cleared.
The extension did not include a goal chance for any of the teams.
It was mostly a wait for the penalties.
After a free kick, Villarreal made it 1-0 after just under half an hour.
Gerard kept Victor Lindelöf away with his hands in the crowd and was able to angle the ball on half volley near goal.
After ten minutes in the second half, Man United equalized to 1-1.
After a corner and a subsequent shot from Marcus Rashford who bounced in the defense, Edinson Cavani stayed ahead and scored 1-1.
The case was long reviewed for offside before it was approved.
Rashford had the great chance
With 20 minutes left, Bruno Fernandes scored the ball from the right to Rashford who ran free.
However that did not end in goal thanks to the magnificent intervention of Gerónimo Rulli, who managed to clear the ball to corner with the tip of his fingers.
A few minutes later, the ball bounced like a pinball in Villarreal's penalty area but away from the dangerous area.
It was United who controlled the match during regular time, but as the extra time approached, the tempo slowed down.
Villarreal made five substitutions during regular time and one during extra time.
Man United made no substitutions during regular time.
The team made five changes during extra time, four from match minute 116 onwards.
Around 9,500 fans, including Man United's legendary coach Sir Alex Ferguson, 79, watched the match on site in Gdansk, Poland.