Sociedad saw their chances of Champions League football recede a little further as they failed to build on a seventh-minute strike from Gonzalo Castro, conceding the equaliser just before the hour mark as Oriol Riera headed in for the hosts.
The result leaves Osasuna in the drop zone while Sociedad are six points off fourth-placed Athletic Bilbao with seven left to play.
It began so well for Sociedad, who had a chance for Carlos Vela inside the opening minute before Castro opened the scoring, firing a low shot into the net from Vela's pass.
Riera headed wide for Osasuna but Sociedad were still on top, and Andres Fernandez had to make a good save to keep out Imanol Agirretxe's header in the 25th minute.
Set-pieces were giving Osasuna opportunities but Riera missed a couple of them, the latter when he headed over from six yards out from a Roberto Torres free-kick, but the hosts were growing in confidence as half-time neared, creating a pair of chances for Miguel De las Cuevas which he could not get on target.
The second half began with a great chance for Sociedad but David Zurutuza missed the target from close range before an ambitious long-range effort from Inigo Martinez found the crossbar.
Torres fluffed his lines with a mis-hit shot for Osasuna in the 55th minute but the equaliser was moments away, arriving when Riera rose to meet a Torres free-kick and divert it into the net.
Sociedad were close to an instant response but Fernandez blocked Castro's header before Alberto De la Bella fired wide on the follow-up.
There were chances at both ends but little on target as nerves began to tell before Osasuna were presented a late chance to win it, Cristian Lobato's shot being diverted over before Claudio Bravo blocked Francisco Silva's shot in stoppage time.