Sevilla got off to a fine start when Papu Gomez put them in front in the third minute, firing into the bottom corner with one touch after latching on to a through ball from compatriot Erik Lamela.
They scored again in the 15th through an absurd own goal from Toni Lato, who blocked a cross from outside the area which bounced awkwardly and ended up floating past a fellow defender and into the net, flummoxing keeper Giorgi Mamardashvili.
Sevilla struck for a third time in the 22nd minute following more careless defending from the visitors, who were caught out by a quickly taken free kick from Fernando which looped over their defence and Rafa Mir raced after it to calmly lob over Mamardashvili into the net.
Valencia responded soon after with a goal from striker Hugo Duro and managed to gain some control in the second half but never looked like getting back into the game and threatening Sevilla's lead.
Sevilla are third in LaLiga with 11 points from five games while Valencia are fourth with 10 points from six.