The Valencia-based club have 17 points and are in second spot only on goal difference behind Barcelona who cruised to a 3-0 win over Racing Santander on Saturday while Real Madrid are a point further back despite a 4-1 mauling of Real Betis.
Levante, who escaped relegation by just two points last season, were quickly ahead yesterday from a Jose Barkero shot on 14 minutes that took a deflection off Malaga midfielder Enzo Maresca.
Disaster struck for Malaga when goalkeeper Willy Caballero received a red card on 28 minutes for handling outside of his area.
From Barkero's resulting free-kick Juanlu Gomez was quickest to react to the parried save of substitute goalkeeper Ruben Martinez to get the second.
Malaga's goalkeeping problems continued in the 40th minute when Ruben failed to come for a routine long ball allowing Arouna Kone to nip in for the home team's third goal.
Levante could have added more in the second half but will be content with the three points over a Malaga side who sat in fourth place before the weekend's games.
"It's very difficult to win in the first divison and more so to win five consecutive games, but that is what Levante have achieved. I never expected this result," said Levante coach Juan Ignacio Martinez.
Unbeaten Sevilla kept up the pressure at the top with a 2-1 victory over bottom club Sporting Gijon.
A spectacular drive from Manu del Moral on 15 minutes and a header from Martin Caceres on 57 minutes were enough to lift Sevilla into fourth position, two points behind Barcelona and Levante.
David Barral got a consolation goal for Gijon on 64 minutes, defeat leaving the north coast club rock bottom with one point.
At Camp Nou on Saturday Lionel Messi's brace and a rare header for captain Xavi Hernandez were enough to seal the points for Barcelona.
The result was never in doubt and Barca were able to take their foot off the pedal towards the end with one eye on Wednesday's Champions League match at home to Czech side Viktoria Plzen.
However, they will be without defender Gerard Pique who limped off with a right thigh injury and will be out for at least two weeks.
For Barca's first goal on eight minutes Andres Iniesta turned cleverly in the area to find Messi who skipped around Santander goalkeeper Antonio Rodriguez 'Tono' to push the ball into an open net.
Barcelona's second came 19 minutes later from the head of Xavi after good work and a fine cross from Pedro Rodriguez on the left wing.
On 67 minutes, Iniesta received a pass from Messi on the left hand side of the area and beat off two defenders with a magical feint before striking the post only for Messi to pounce to convert the rebound.
Real Madrid striker Gonzalo Higuain hit his third hat-trick in four matches as Real eased past Betis on the day that Cristiano Ronaldo played his 100th match for the club.
All the goals came in the second half with Madrid ahead within 30 seconds of the restart.
Marcelo's long, raking pass found Ronaldo's attacking run down the left and one touch was all he needed to present Higuain with an open goal.
Kaka then placed a curling right-footed shot into the bottom right corner in the 59th minute.
Jorge Molina pulled a goal back for Betis from close range on 69 minutes, but any hope Betis had of taking anything from the game lasted less than a minute.
Angel Di Maria found Higuain, who hit three goals for Argentina against Chile last weekend and three the week before against Espanyol, with a beautifully weighted pass from the right wing that left the Argentine to neatly take the ball round Betis keeper Casto Espinosa and finish into an open net.
On 73 minutes Higuain completed the rout when his compatriot Di Maria again found him with a defence-splitting pass that he chipped over the oncoming Casto.
Valencia missed out on joining Madrid on 16 points after drawing 1-1 at Mallorca.
A Tomer Hemed penalty for Mallorca in added time levelled after French international defender Adil Rami had scored from close range on 38 minutes for Valencia.