Ignacio Camacho's unfortunate own-goal proved enough to tip Saturday night's Andalusian derby in Granada's favour.
The hosts at Los Carmenes were the better side throughout but needed a mistake from Malaga midfielder Camacho to book them the win that brings them within three points of safety.
Granada's 1-0 triumph was their first in five attempts while seventh-placed Malaga missed an opportunity to notch a third straight Primera Division victory.
Javi Marquez gave Malaga goalkeeper Carlos Kameni food for thought with a free-kick in the 11th minute and it was not long before Emanuel Insua blasted over the Cameroonian's bar.
Granada, 19th in the table, kept turning the screw and Piti got Kameni working before Marquez came knocking again with a left-footed effort following a defensive scramble by Malaga.
Los Boquerones finally bit back when Samu Garcia shot wide at the end of a flowing team move and the Malaga-born striker shot over the bar five minutes before the break.
Granada's last move of the half had seen Robert Ibanez drive Youssef El-Arabi's pass straight down Kameni's throat, and the hosts went into half-time knowing they should have taken the lead.
Malaga would do them a favour in that regard when play resumed.
In the 57th minute Camacho was in the wrong place as Ibanez's header cannoned off his back before beating the surprised Kameni.
Samu Castillejo tried to spare his team-mate's blushes by equalising after the hour mark but Oier was wise to the move and got gloves to the ball.
Camacho stepped up himself and went one better, hitting the bar at the end of a fine solo run, but Malaga would soon run out of ideas.
Granada then went all out in pursuit of the second goal and Riki went close with a header before Jhon Cordoba repeated the trick with 10 minutes remaining.
Abel Resino's men kept on pushing but they would not score a goal of their own making, with Camacho's unfortunate moment enough to guarantee them all three valuable points.