The Argentine struck twice in the first half before Valentin Stocker added a late third to put Murat Yakin's men in complete control ahead of their trip to Mestalla
In a game played behind closed doors at St Jakob-Park because of crowd trouble in the victory at Red Bull Salzburg in the last 16, the hosts made light of the lack of home support to give themselves a great chance of a spot in the last four 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.
Valencia, who were perhaps lucky not to be reduced to 10 men in the early stages when Philippe Senderos bundled into David Degen inside the area, offered very little going forward in the first half but were improved in the second.
Eduardo Vargas squandered their best opening midway through the second half, heading wide from eight yards after getting on the end of Fede Cartabia's cross from the left.
Despite enjoying much of the ball in the closing stages, Juan Antonio Pizzi's side could not break down their stubborn opponents and now have it all to do at Mestalla next Thursday.
Basel felt they should have had a penalty in the 11th minute when Senderos collided with David Degen as he bore down on goal, but referee Martin Atkinson waved away the home side's vociferous appeals.
Marcelo Diaz tested Vicente Guaita from 20 yards seven minutes later but the Valencia goalkeeper was equal to his effort, recovering well to smother the ball at the second attempt.
The hosts were dominant and Guaita was called into action again 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 Argentine 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 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 Sommer parried Seydou Keita's effort before Basel broke forward, captain Stocker coolness personified as he dinked the ball over the advancing Guaita to leave the Swiss outfit with one foot in the semi-finals.
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