David Barral headed the only goal of the game for the home side from a set-piece corner in the 19th minute as Levante got a much-needed victory after losing six of their previous seven in La Liga.
Barral did well to find the net as he leapt the highest among a mass of bodies to nod Andreas Ivanschitz's corner past Malaga goalkeeper Willy Caballero at the far post.
The result lifted Levante into 10th place in the overall standings, while Malaga slipped to 14th.
There was not much between the two sides, as you might expect for a middle of the table clash, but Duda had a good chance to put Malaga ahead in the sixth minute when his 20-yard curling effort was blocked by Loukas Vyntra.
Vyntra again denied Duda, this time from slightly closer range before Barral forced a save out of Willy at the other end.
Barral, who was starting to become a pest as far as Malaga were concerned, then curled a fantastic strike from 25 yards which was blocked by Sergio Sanchez.
He did not have to wait long to break the deadlock, though, as five minutes later he got his name onto the scoresheet with a well-taken header from Ivanschitz's corner from the right-hand side.
Other chances were few and far between in the first half, with Ruben Garcia blasting over from 30 yards before Malaga striker Samu sent a low shot wide of the target and Ignacio Camacho had an effort blocked by Nikos Karabelas.
The second half told a similar story, with both sides unable to finish off their chances.
Francisco Portillo had a shot blocked by Juan Francisco Garcia and Levante's Ivanschitz had a 58th-minute long-range strike caught by Willy.
Malaga defender Eliseu had the best chance of the half when he drilled a shot from the edge of the area, but Garcia was up to the task and made the crucial block to preserve his side's slender lead, which they held onto until the final whistle.