Jose Salomon Rondon scored the only goal as Malaga leapfrogged Levante into fourth place in the Primera Division.
The hosts had by far the better of the opening period but it took them until six minutes after the break to take the lead when Rondon got the merest of touches to Joaquin's cross to divert the ball into the far corner.
Arouna Kone nearly brought the visitors level as he prodded just wide at the near post and after Isco, Rondon and Sebastian Fernandez passed up chances to seal the three points for Malaga, Nabil El Zhar came within inches of snatching a draw with the last kick of the game but his volley flew just over as the home side held on for the points.
Both sides came into the game after back-to-back wins but it was Malaga who appeared the more confident as Levante played extremely cautiously in the first period.
However, the visitors tactics frustrated the hosts as their best efforts early on came from long-range shots by Isco and Santi Cazorla that went just wide.
Joaquin then forced Gustavo Munua into his first serious save with another shot from distance before Rondon's goalbound header was hooked over his own bar by Gustavo Cabral.
The opener did eventually arrive for the home side just after half-time as Joaquin's free-kick into the area was flicked beyond the reach of Munua by Rondon for his seventh goal of the season.
The goal forced Levante onto the front foot and they were nearly level within 10 minutes as Kone got to Pedro Botelho's cross ahead of Willy Caballero but just could not direct the ball on target from a narrow angle.
Malaga should then have doubled their advantage on a number of occasions but Isco fired straight at Munua after a wonderful solo run had taken him past the Levante defence before Rondon headed over and Fernandez wastefully fired wide.
And those misses nearly cost them as Caballero had to make a smart stop to deny Cabral and El Zhar's last-ditch attempt dipped just over the Argentinian's crossbar.
