Despite playing in front of an empty stadium, the home side secured a three-goal advantage in the first leg of its quarterfinal clash against the Spaniards
The game was played behind closed doors at St Jakob-Park after Basel fans' misbehavior in the victory at Red Bull Salzburg in the last 16. However, the hosts made light of the lack of home support to give themselves a great chance of a spot in the semifinals for the second year in succession.
A first-half brace from Matias Delgado - a rasping effort in the 34th minute and a beautifully guided close-range finish four minutes later - and Valentin Stocker's impudent stoppage-time chip put Murat Yakin's side in complete control of the tie heading into the second leg in Spain next week.
Basel felt they should have had a penalty in the 11th minute when Philippe Senderos collided with David Degen as he bore down on goal, but referee Martin Atkinson waved away the home side's vociferous appeals.
The hosts were dominant and Vicente Guaita was called into action in the 24th minute, brilliantly tipping Fabian Schar's fizzing strike from distance around the post.
He could do nothing about Delgado's opener, however, the Argentinian picking up Philipp Degen's ball before thumping a shot beyond the despairing dive of the keeper into the bottom left-hand corner.
Four minutes later it was two, Delgado touching home Stocker's devilish cross from the left.
The visitors showed signs of improvement after the break, Paco Alcacer and Eduardo Vargas both fluffing chances to convert from Cartabia's low cross from the left.
Vargas then stretched Basel's Yann Sommer for the first time in the 55th minute, the keeper parrying away the striker's effort that bounced awkwardly in front of him.
The Chilean ought to have earned his side a crucial away goal in the 69th minute, heading a bouncing delivery wide from close range when completely unmarked.
And Valencia's frustrating evening was summed up at the death as Basel broke forward. Captain Stocker was coolness personified as he dinked the ball over the advancing Guaita to leave the Swiss outfit with one foot in the semifinals.