The hosts registered the first effort on goal when Borja Valle's shot from outside the box in the fourth minute was saved by Geronimo Rulli.
Little happened in the ensuing 15 minutes, with the action concentrated in midfield and tackles from both sides breaking up play.
In the 20th minute, it was Sociedad's turn to attack, Gaztanaga attempting a long-range drive following a corner, but it flew wide of the right-hand post.
The visitors upped the tempo in the final stages of the first half, but Yuri's efforts also failed to break the deadlock.
Josep Sene then missed a sitter for the hosts in the 62nd minute, firing too high from right in front of the goal.
As the minutes ticked on, both teams continued to press forward in a bid to grab what could potentially have been the winner, David Fernandez heading just over in the 74th minute and Yuri also firing wide six minutes later.
Oviedo found themselves having to defend a few goalmouth scrambles in the latter stages of the game, but they did so admirably.
Right at the death, Finnbogason had a great chance to seize the win, but his close-range header flew off target, with the final whistle blowing moments later.