Suso gave the Andalusians the points with a thumping strike in the 81st minute after charging through to collect a Joan Jordan through ball.
The winning strike was the 27-year-old Spain international’s first goal of the season.
Sevilla are six points behind league leaders Atletico Madrid ahead of their top-of-the-table clash at Real Sociedad later on Tuesday.
They are also two points in front of Barcelona, who will again try to get their season back on track when they take to the field at Real Valladolid.
Valencia are 13th just a point above the relegation zone after their sixth consecutive league match without a win.