The winners face Arsenal or Napoli in the semi-finals.
Daniel Wass struck in the first minute of added time to put Valencia in the driving seat ahead of the second leg at the Mestalla, before Goncalo Guedes grabbed his second of the match to leave Villarreal facing an uphill task.
Both sides were awarded penalties in a pulsating first half, with former Arsenal midfielder Santi Cazorla cancelling out Guedes’ opener.
Only 60 kilometres separates the two sides on Spain’s east coast, but Valencia’s 12-place lead in LaLiga over relegation-threatened Villarreal suggested a potential gulf in class.
It was a gulf that threatened to become apparent as the visitors flew out of the blocks and won a penalty in the sixth minute when Guedes cut inside and was upended by Santiago Caseres.
Dani Parejo’s penalty was well saved by Andres Fernandez, but Portugal winger Guedes reacted first to bury the rebound and grab a crucial away goal.
But the Yellow Submarines began to get a foothold in the match and threatened an equaliser when Cazorla’s free-kick was inches wide on the half-hour mark.
The hosts were level six minutes later after Ezequiel Garay brought down former Leicester midfielder Vicente Iborra, giving Cazorla the chance to score from the spot – having missed a crucial penalty last Sunday in the defeat to Real Betis.
Javier Calleja’s side continued their superiority after the break and pressed to take the lead.
Cazorla went close again, but was unable to keep a strike down from the edge of the area while Samuel Chukwueze was twice denied by Valencia keeper Neto before the hour mark.
Valencia though finished the game the stronger. Wass threatened seven minutes from time but his shot trickled harmlessly wide.
But the Dane made no mistake in the first minute of added time, latching on to Jose Gaya’s low cross to bury from close range.
And Guedes poked the ball past Fernandez to give Valencia a commanding advantage.
Villarreal out to set aside relegation worries to reach Europa League semi-final