Diego Marino, for the home side, was the busier of the two goalkeepers and his save from Jose Toche seconds after half-time proved a crucial moment.
Levante’s sporadic threat came mostly from set-pieces, but David Barral’s finishing was wasteful and they failed to seriously test visiting keeper Fabricio.
They are one place and two points above the bottom three with the rest of the weekend’s fixtures still to unfold, while 15th-placed Depor are another point to the good.
Levante could have taken the lead inside the first minute, but Barral headed Andreas Ivanschitz’s corner wide.
They were on the back foot for most of the first half, though, and Ivan Cavaleiro shot wide from the edge of the box before Isaac Cuenca drew a save from Marino.
Cavaleiro sent another long-range effort over and then saw his header saved by Marino.
He turned provider in stoppage time when his corner was met by defender Sidnei, who headed over.
The pressure continued early in the second half as Marino made close-range saves from Toche and Sidnei.
A free-kick at the other end provided some respite and Ivanschitz again picked out Barral, who flashed a right-foot shot wide.
Victor Casadesus headed over before Levante again went quiet as an attacking force.
A Depor breakaway ended with Cuenca shooting wide and when Alex Bergantinos headed Luisinho’s left-wing free-kick over the bar, the final chance was gone.