First-half goals from Jose Luis Morales and Giuseppe Rossi, the former Manchester United striker's effort coming from the penalty spot, were added to be a late strike from Joan Verdu as the hosts claimed a 3-0 success over their mid-table opponents.
The victory, their first in four games, was enough to lift them above Granada on goal difference and only two points away from safety.
Levante started with plenty of intent and should have taken the lead inside five minutes through Deyverson.
Morales worked some space on the left and clipped in a perfect cross for Deyverson, who lost his marker in the six-yard box but saw his header kept out by goalkeeper Vicente Guaita's leg.
Four minutes later Morales opted to go alone and was rewarded with his sixth league goal of the season.
The winger burst in off the flank, beating both Juan Rodriguez and then the lunging Santiago Vergini, before poking past Guaita with a fine finish into the corner.
Levante's lead was doubled before the break thanks to Rossi's cool penalty after Vergini was again beaten by Morales.
The Sunderland loanee clattered into him after a loose touch backwards and was given a yellow card for the foul before Rossi stroked the spot-kick right into the corner.
Getafe had opportunities to get back into the game in the second half but Alvaro Vazquez was guilty of wasting their best two, hitting one against the post from just six yards out with goalkeeper Diego Marino stranded.
And Levante made it 3-0 with nine minutes remaining as Morales set up Verdu, who rode a weak challenge from Damian Suarez before dinking in at the near post to consign Getafe to a fifth straight loss.
