A solitary goal by Odion Ighalo saw off Malaga and handed Granada a huge boost in their bid to avoid relegation from the Primera Division.
The Nigerian's goal midway through the first half took Lucas Alcaraz's side further clear of the drop zone and struck a blow to Malaga's already slim hopes of reclaiming fourth spot from Real Sociedad.
Granada began the game just a point clear of the bottom three and on a high from beating Espanyol away from home in their last game.
And their sense of urgency was evident in the first half.
Yacine Brahimi and Ighalo came close to scoring after 12 minutes, but neither player could take advantage of a scramble in the Malaga area and goalkeeper Willy Caballero cleared the danger.
The Argentinian then produced a great stop to deny Nolito, getting down low to palm the ball away.
At the other end, Isco and Vitorino Antunes had attempts on goal, but neither player could get their shots on target.
Granada took a deserved lead on 28 minutes.
Brahimi got down the right wing and put in a cross which the Malaga defence should have dealt with, but Ighalo got ahead of Martin Demichelis and struck the ball first time over Caballero and into the net.
Youssef El-Arabi came close to doubling the lead before the break, but pulled his shot just wide of the far post, while Isco threatened to equalise when he cut inside from the right wing, but failed to strike the ball cleanly and his shot rolled wide.
Malaga were an improved outfit in the second half and forced Granada to retreat and defend their lead.
The hosts did well to keep their opponents, and particularly the menacing Isco, at bay and could have wrapped the game up through a counter-attack, but Carlos Aranda could only shoot straight at Caballero, while Nolito skied the rebound.
Malaga continued to press and almost got an equaliser when Antunes' attempted cross came back off the bar, but despite their superior possession and constant pressure they were unable to find the net.