Although Valencia forward Kevin Gameiro struck the underside of the bar in the second half, Sevilla utterly dominated the game, firing 17 shots at goal to Valencia's four but repeatedly missed the target and were thwarted by visiting goalkeeper Neto.
They also had a penalty appeal deep in stoppage time turned down and had a goal correctly ruled out for offside in the final incident of the game.
The victory took Valencia up to sixth in the La Liga on 43 points after 29 games, level with Sevilla who slipped to seventh.
Both sides are three points behind Getafe, who lost 2-0 to Leganes on Saturday but still occupy fourth place.
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(Reporting by Richard Martin; Editing by Toby Davis)
