Alvaro Negredo fired the Andalusian side into the lead in the 34th minute before Salvi Sanchez made it 2-0 in the 73rd. Alessio Lisci, Levante’s coach, was sent off in the 76th minute.
The result means that Cadiz have gone up to 18th in the league table and are just two points from Mallorca and safety. Levante remain rooted to the bottom of the table, nine points from safety.
Cadiz play Valencia next in the quarter-final of the Copa del Rey before going to the Balearic Islands to take on Mallorca. Levante travel to the Coliseum Alfonso Perez to play Getafe next before hosting high-flying Real Betis.
Both Cadiz and Levante are in the midst of a tight relegation battle. The latter look beyond saving, being honest, but the former could climb out of the drop zone if they beat Mallorca.