After a tight opening, the away side took the lead five minutes before the break courtesy of a tidy finish from former Newcastle United striker Obafemi Martins.
Deportivo also had a player dismissed in the second half, however, when their goalkeeper Dani Aranzubia felled Martins outside the box.
Despite constant pressure from the home side, it was Levante that wrapped up the points with a late strike from Jose Barkero.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary below.
Deportivo: Aranzubia; Marchena, Ze Castro, Ayoze, Laure; Valeron, Camunas, Bergantinos, Dominguez; Riki, Gama
Levante: Munua; Juanfran, Navarro, Lopez, Ballesteros; Juanlu, Iborra, Barkero, Michel; Martins, El Zhar