The game was as good as over inside the opening half-hour as Depor struck three times through Juan Carlos Valeron, Luis Pizzi and Nelson Oliveira.
Levante pushed but could find no way back after that and Bruno Gama put the icing on Depor's cake with a fourth goal late on as the in-form Galicians claimed their biggest win since 2011.
It is also a victory that provisionally lifts them out of the relegation zone for the first time since November.
They looked destined for an immediate return to the Segunda Division just over a month ago after finding themselves rock-bottom and nine points adrift of safety, but their run of four successive wins has now seen them provisionally climb up to 16th above Real Zaragoza and Granada.
Both Zaragoza and Granada still have to play this weekend but, as they face Barcelona and Atletico Madrid respectively tomorrow, Depor will feel confident they can remain out of the bottom three .
Depor coach Fernando Vazquez had to watch today's clash from the stands due to a touchline ban but that did not seem to bother his team as they stormed into a 3-0 lead.
Veteran playmaker Valeron put them ahead after just 12 minutes and Portugal international Pizzi doubled the advantage eight minutes later with a thunderous strike from the edge of the box.
Depor continued to press and Oliveira saw a shot fumbled by Gustavo Munua before the on-loan Benfica forward made it 3-0 in the 28th minute with a left-footed strike.
Shell-shocked Levante made an immediate substitution, sending on Michel for Pape Diop, and they set about trying to get a foothold back into the game.
However, they could not find a way past visiting keeper Daniel Aranzubia, who denied Roger, Juanlu and Christian Lell in the second half, and Depor added a fourth goal when another of their Portuguese contingent Gama slotted home Valeron's pass in stoppage time.