Juventus Mattia De Sciglio gestures as Villarreal s Pau Torres, fourth from right, celebrates with his teammate Gerard Moreno after scoring his side s second goal during the Champions League, round of 16, second leg soccer (AP)
Substitute Gerard Moreno converted a penalty, then Pau Torres was left unmarked to redirect in a corner before Arnaut Danjuma added another spot kick.
Villarreal advanced 4-1 on aggregate as two-time winner Juventus was eliminated at home in the round of 16 for the third consecutive season.
It's the first time in 13 years that Villarreal has reached the last eight.
In Wednesday's other match, defending champion Chelsea advanced 4-1 on aggregate after a 2-1 win at Lille.
The draw for the quarterfinals will be held Friday.
Liverpool, Bayern Munich, Real Madrid, Manchester City, Atletico Madrid and Benfica also advanced to the last eight.
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