The win came thanks to goals from Simone Zaza and Rodrigo, whose second-half penalty restored the lead following an equaliser early in the second half from Alexis.
Zaza fired a powerfully struck opener in the 34th minute, collecting Andreas Pereira’s cross from the right and driving the ball high into the near top corner.
Alexis headed a leveller from a corner in the 49th minute, but a deliberate handball close to his own goal from Alaves defender Rodrigo Ely then proved costly.
It allowed Valencia’s Rodrigo to slot in the 66th-minute penalty that secured three points, moving Valencia at least temporarily to just one point behind leaders Barcelona.
Barcelona were due in action later on Saturday, with an evening kick-off at Athletic Bilbao.