The Andalusian side had slumped to within four points of the relegation zone after losing four of their last five matches but they picked up a valuable victory on Friday night thanks to Jose Recio's brace and further goals from Jeison Murillo and Youssef El Arabi .
That gave Granada only their third league win at the Estadio Los Carmenes this campaign - having lost the other seven matches - and pushed them up to ninth in the standings.
Valladolid, meanwhile, drop into the bottom three following the loss.
Granada started well and Piti drew a parry out of visiting goalkeeper Diego Marino before Murillo opened the scoring in the 12th minute with an acrobatic overhead kick.
It was 2-0 10 minutes later when Recio volleyed home from Fran Rico's cross, a goal which came immediately after Marino had done well to tip over Piti's 25-yard free-kick.
Valladolid tried to find a foothold back into the game and Victor Perez was denied by Roberto Fernandez in the home goal just after the half-hour mark.
The visitors' hopes of getting anything out of the game disappeared in the 55th minute, though, when they found themselves 3-0 down as Recio notched his second with a right-footed shot from the edge of the box.
Granada then added a fourth goal 12 minutes from time to wrap up their biggest league win since 2010. Diego Mainz got his head on Recio's corner from right and El Arabi was on hand to turn the ball in from close range.