Croatian striker Duje Cop gave Malaga the lead in the 30th minute with a near-post finish barely a minute after Levante striker Mauricio Cuero had a goal harshly ruled out for offside.
Jose Luis Morales levelled in the 42nd minute but Malaga finished the game stronger and deserved to take the lead again in the 89th through Cop which put Levante on the brink of relegation.
Chory Castro delivered the final nail in the coffin with a powerful finish from the edge of the area in stoppage-time.
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The Valencia club are bottom of La Liga on 29 points, six points behind Getafe, Sporting Gijon and Rayo Vallecano with two games remaining.
They have collected just six points away from home this season, winning only one game on their travels.
Levante were promoted to La Liga in 2010, their centenary year, and two years later qualified for European football for the first time.
They reached the round of 16 of the Europa League before being knocked out by Russian side Rubin Kazan.
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