Levante, who are in the race for a berth in Europe's elite club competition despite having one of the oldest squads in the league, snatched victory at the Cornella Stadium when Ruben Suarez's 89th-minute free-kick was deflected into the net.
Valdo, a former Espanyol player who also had a stint at Real Madrid, put Levante ahead against the run of play in the 25th.
Nigerian forward Kalu Uche came off the bench to grab the equaliser 15 minutes from time, performing his customary back-flip in celebration, before Suarez struck the winner to give Levante their first victory in nine games since mid-December.
A beaming Suarez said in an interview with Spanish television that Levante's priority was still to avoid being relegated, with only nine points separating fourth from 17th.
"Obviously the more time we spend near the top of the table the better," the 33-year-old midfielder added.
"Our goal is still the same, which is avoiding the drop, so we are keeping our feet on the ground."
The Valencia-based club have 35 points from 24 matches, one more than fifth-placed Malaga, who thumped bottom side Real Zaragoza 5-1 in the earlier kick-off.
STORMING OUT
Zaragoza took the lead at Malaga but ended up on the wrong end of a drubbing and remain rooted to the bottom of the table with just 15 points from 24 matches.
They are 11 points adrift of the safety zone.
A furious Manolo Jimenez, who was hired as coach to replace the sacked Javier Aguirre at the end of last year, said he was "ashamed" by his team's performance.
"Until their second goal Zaragoza played well," he told reporters at a brief post-match news conference.
"But I am not going to finesse the truth any longer," he added, before twice repeating "I feel ashamed" and storming out of the room.
Fellow strugglers Racing Santander and Sporting Gijon drew 1-1 in Santander and are 18th and 19th respectively, while Real Betis and Getafe played out a 1-1 stalemate in Seville that left them in 11th and 13th.
