The two clubs entered the match in 20th and 19th respectively and while that remains the case, Levante are now just one point behind Las Palmas and just two behind 17th-placed Rayo Vallecano.
A tight opening 20 minutes saw neither side create a chance of note, but the hosts took the lead in the 25th minute when Jose Morales converted from close range after Verza had struck the post with a free kick.
The visitors were made to pay for their missed opportunities when Jefferson Lerma set up Deyverson to make it 2-0 Levante in the 47th minute, but Las Palmas had one back less than two minutes later when Willian Jose converted a cross from Simon.
Morales scored his second just past the hour to strengthen Levante's grip on the three points, but Las Palmas again hit back three minutes later when Jose capitalised on some poor defending to fire home his second of the match for 3-2.
Levante were treated to their new signing Rossi for the final 15 minutes and the Italian almost marked his debut with a goal, but his low strike late on was kept out by Javi Varas.
Las Palmas had chances to snatch a point late on through Roque Mesa and Morales, but the home side, who had Deyverson sent off late on for a second bookable offence, held on to secure three vital points. body check tags ::