The two evenly-matched sides enjoyed plenty of half-chances throughout the game, though a mixture of poor finishing and solid defending from both teams kept things tight.
Soldado made the breakthrough from a corner six minutes into the second half, with Adil Rami's lovely flick-on completely wrong-footing the Sevilla defence and giving the Valencia striker the simplest of tap-ins from three yards.
Late Sevilla sub Miroslav Stevanovic almost levelled things four minutes from time after controlling Ivan Rakitic's pass on his chest before forcing Diego Alves into a superb diving save.
But the resulting counter-attack saw Valencia wrap up all three points. First, Soldado picked up a long ball, rounded Sevilla goalkeeper Diego Lopez and saw his shot cleared off the line by Gary Medel. His disappointment did not last long: from the resulting corner, Soldado was on hand as the ball went loose and he was able to head home a second goal from almost point-blank range.
The result boosts Valencia's hopes of getting into contention for a European spot as they climb to seventh spot, just a point behind fourth-placed Malaga, while 12th-placed Sevilla will be looking nervously over their shoulders as they were left just six points above the drop zone.