Rubén García converted a penalty kick awarded by video review in the 81st minute and Iñigo Pérez scored from inside the area in the 84th to give the hosts their first league win since December.
Osasuna had won only one of its last eight league games. It moved to 10th in the 20-team standings.
It was the third straight defeat for Levante, which dropped to 13th.
Osasuna saw forward Ezequiel “Chimy” Ávila leave the match early in the second half with what appeared to be a serious knee injury.