Helder Postiga scored his first goal for Los Che after 10 minutes, but Espanyol responded with headed goals from David Lopez and Christian Stuani to take a deserved lead, which they never really looked in danger of surrendering, before substitute Thievy Bifouma made sure of the points in the 89th minute.
The hosts made the brighter start, and Simao Sabrosa could have given them the lead with less than a minute gone when he met a cross from Pizzi, but mishit the ball and sent it just wide of goal.
Pizzi caused further danger five minutes later on the flank, but his cross just escaped the grasp of Stuani. It was then Diego Colotto's turn to squander a chance, failing to aim a header on target.
Despite the hosts' early dominance, it was the visitors who took the lead.
Jonas received the ball from Adil Rami with his back to goal, took it on the chest and played in Postiga, who made no mistake.
Javier Aguirre's side did not allow themselves to become disheartened by going behind, however, and kept pushing for a goal of their own.
Sergio Garcia almost levelled from a header after a cross from Simao, but directed the ball lost wide of the far post.
A few minutes later Lopez got the goal the hosts deserved, losing his marker Jeremy Mathieu - who had a torrid time playing at left-back - to head the ball in at the near post from a corner from Simao.
However, the former Portugal international was fortunate to remain on the pitch after elbowing Rami in the face shortly before the break.
Espanyol took the lead moments after the re-start, again taking advantage of lacklustre defending from Valencia at set pieces. This time it was Juan Rafael Fuentes who hooked the ball in, from a free-kick, and Stuani rose high above the defence to head the ball right into the top corner.
Valencia's best chance to equalise fell to Banega, who ran onto an exquisite pass by Jonas, but the Argentinian was unable to keep his shot down as he faced pressure from an Espanyol defender.
With time running out for Miroslav Djukic's side, who never found their rhythm, Thievy killed off the tie by finishing a brilliant move that he had started.
The Frenchman, who had replaced Sergio Garcia on 72 minutes, picked up the ball in space in Valencia's half, beat two defenders and switched to fellow substitute Manu Lanzarote on the right hand side of the box. Lanzarote outfoxed Guardado and Javi Fuego before cutting the ball back to Thievy, who lashed it into the far corner.
Aguirre's side remain unbeaten, while Djukic tasted defeat for the first time as Valencia boss.