Brazilian forward Jonas scored the only goal of the game in the 33rd minute to put Valencia in the driving seat in the all-La Liga encounter.
In the night's other game, second-tier Cordoba served up a surprise by defeating 10-man Espanyol 2-1.
Espanyol were leading thanks to Sergio Garcia's 38th-minute strike when goalkeeper Francisco Casilla was sent off for a foul on Jose Diaz in the box.
Substitute goalkeeper Cristian Alvarez looked like being Espanyol's hero when he saved Diaz's resulting penalty kick, but Cordoba mounted a late rally to stun their visitors.
Borja Garcia's deflected 81st-minute strike started the fightback, while the win was sealed in the 85th minute when Carlos Caballero fired home.
The second legs of both of Thursday's matches will be played on Wednesday.