Joaquin Caparros' men looked more likely to be embroiled in a relegation fight after losing six of seven league matches around Christmas, but since suffering a 2-0 derby defeat to Valencia on January 4 they have compiled an unbeaten eight-match run to storm up the standings.
Their latest success came courtesy of first-half goals from Papakouli Diop and Ruben Garcia, although they were made to sweat for the points after losing Victor Casadesus to a red card in the 60th minute.
Osasuna could not find a way back into the match, though, to leave Levante seventh and within seven points of sixth-placed Real Sociedad, who face a tough trip to Sevilla on Sunday.
Osasuna, meanwhile, remain in mid-table after seeing their recent good run come to an end.
The Pamplona side had earned seven points from their previous three games - including stunning title hopefuls Atletico Madrid 3-0 last week - and they started promisingly on Saturday with Alvaro Cejudo firing an opening over inside three minutes.
However, just a minute later Osasuna found themselves a goal down when Senegal international Diop picked up a pass from Andreas Ivanschitz and drilled home from the edge of the box,
Osasuna tried to find an immediate response and it needed a good parry from home keeper Keylor Navas to turn behind Oriol Riera's shot.
Emiliano Armenteros then saw a shot go wide for the visitors before Levante started to take more control towards the end of the period, with Nikos Karabelas and David Barral trying their luck.
Neither of those efforts found a way past Osasuna keeper Andres Fernandez, but that was not the case in the 42nd minute when Ruben made it 2-0 with a right-footed finish from Juanfran Garcia's free-kick.
That left Levante in control but their position of dominance was threatened when Victor was handed his marching orders on the hour, the striker dismissed for a foul on Alvaro Cejudo.
Osasuna pushed forward after that as they sought to take advantage, but they could not beat Navas, who produced saves to deny Riera and Armenteros before parrying an Javier Acuna shot deep into stoppage time to ensure Levante will make next week's daunting trip to Real Madrid on a high.