Jose Barkero's deflected shot gave the hosts the perfect start after 13 minutes and things went from bad to worse for the visitors after half an hour.
Firstly goalkeeper Willy Caballero was sent off for handling outside the area and then, as the resulting free-kick rebounded off the wall, Juanlu fired the loose ball in for the second.
Arouna Kone scored the third before half-time following a shocking error from substitute keeper Ruben Martinez and Levante should have added to their tally in the second period but Ruben Suarez inexplicably shot over from 10 yards when perfectly placed.
Both sides came into the game in the Champions League places after a great start to the campaign but it was Levante who again demonstrated their ruthlessness in the final third in a strange first-half.
Juan Ignacio Martinez's men have enjoyed the least amount of possession of any side in La Liga this season despite being joint top and they continued that pattern by being three up despite having only 38% of the ball.
After a lacklustre opening 10 minutes the hosts took the lead as Juanfran got to the by-line on the left and cut the ball back for Barkero whose shot on the turn was deflected past his own keeper by Enzo Maresca.
The game then developed into the expected pattern as Malaga controlled the ball but struggled to breakdown an extremely well organised Levante defence.
Santi Cazorla nearly unpicked the lock with a fine through ball for Joaquin but Gustavo Munua was out quickly to smother the ball at the winger's feet.
Moments later Levante all but sealed the three points as Caballero was harshly dismissed as he tried to clear a ball over the top for Kone.
The ball did appear to strike the keeper's hand but it was difficult to tell whether it was outside the box and in any case it was dubious as to whether he had denied a clear goalscoring opportunity.
The loss of a man was compounded for Malaga as Barkero's free-kick rebounded to Juanlu and he smashed the ball past Ruben from the edge of the area.
Five minutes before half-time Kone did get his goal in a similar move to the one that saw Caballero sent off.
This time Ruben tried to wait on the ball to enter the area before collecting and the Ivorian nipped him to round him and slot into the empty net.
Manuel Pellegrini withdrew Cazorla and Ruud Van Nistelrooy at half-time in an attempt at damage limitation and the second-half was played at a pedestrian pace.
Suarez should have added the fourth with 15 minutes remaining but somehow shot over when Valdo's cut-back fell to him perfectly in the middle of the goal only yards out.