The first chance fell to hosts Osasuna after 11 minutes when Oriol Riera got the better of his marker but could not find the target.
Five minutes later Riera came close again when his accurate header was clawed out by Keylor Navas.
Next to try his luck for Osasuna was Emiliano Armenteros, who pounced on a mistake by Navas but could not beat the Levante keeper.
Just before half time Levante had an opening to steal the lead but Baba Diawara failed to head Ruben Garcia's cross on target.
Midway through the second 45 minutes they thought that they had taken the lead when Diawara rounded Andres Fernandez and passed the ball at the unguarded goal. The ball looked like it was going in until Jordan Loties slid in to keep the scores level.
Ten minutes later the away side were again inches away from the opening goal when Pape Diop's header hit the crossbar.
The Granotes' pressure eventually paid off with two minutes left on the clock when Loties brought down Garcia in the area.
Diop stepped up and saw his spot kick saved by Fernandez, with the rebound falling kindly for substitute Xumetra to tuck home.
In the dying moments it got worse for Osasuna as Alvaro Cejudo was sent off for a second yellow card.
Three points move Levante up to eighth in the table, while Osasuna remain in the bottom three.