Sociedad's Mikel Oyarzabal cancelled out Adrian Lopez's first-half penalty for the visitors to leave them fourth on 47 points from 28 games, one point ahead of fifth-placed Getafe who are chasing the last qualifying spot for next season's Champions League.
Getafe slumped to a 2-1 defeat at Granada on Friday, but Real failed to make the most of that slipup as they seemed to lack inspiration without fans creating an atmosphere, with all matches being played behind closed doors.
The result left Osasuna in 11th place on 35 points.
The hosts dominated possession in the first half but they failed to find space and they were punished in the 29th minute when the visitors were awarded a penalty following a Robin Le Normand handball.
Lopez converted the spot kick to put Osasuna in front and they went close to doubling the tally on the stroke of halftime when Inigo Perez's attempt went just over the bar.
Real equalised on the hour. Willian Jose dragged the defence out to the flank and crossed for Oyarzabal, who found the back of the net with a low shot.