Spain international striker Roberto Soldado got the only goal on 55 minutes to move his side into the top half of the league, while Osasuna remain in 16th position.
Malaga thrashed Granada 4-0 to move into fourth.
Two goals in each half, and some clinical finishing, were enough in a convincing victory for the Costa del Sol side.
Joaquin Sanchez got the first, before Javier Saviola, Ignacio Camacho and former Manchester City player Roque Santa Cruz added the others.
Real Sociedad and Getafe stretched their unbeaten runs to five and four matches respectively with a 1-1 draw in which two headed goals came in the final five minutes.
Angel Lafita put the visitors into the lead, before Carlos Martinez grabbed a point for Sociedad in stoppage-time.