Emiliano Armenteros gave Osasuna a 17th-minute lead with the woodwork preventing the hosts from going even further behind moments later.
Augusto Fernandez headed home an equaliser in the 34th minute and although both sides tested the opposition goalkeeper, there was no further score.
Both sides started the match in desperate need of points going into the winter break with Celta fifth from bottom, two places and one point above their visitors.
Osasuna came into the game after a productive week with a draw last weekend against Real Madrid as well as progress in the Copa del Rey with a two-legged victory against Malaga.
Fabian Orellana had the first effort of the game but his 20-yard free-kick went wide while Alcantara Rafinha's shot from similar distance was comfortably held by Andres Fernandez.
Roberto Torres Morales volleyed past the left post for Osasuna and moments later they were in front.
Oriel Riera's ball from the left found Armenteros in the centre of the penalty area and he fired home into the bottom right-hand corner of the goal.
Javi Gracia's side almost doubled their lead within a minute when Torres fired in a 25-yard shot which came off the post.
Michael Krohn-Delhi's shot was easily thwarted by Osasuna goalkeeper Andres Fernandez but Celta had at least stemmed the flow and almost out of nowhere they were level.
Fabian Orellana played a short corner to Alcantara Rafinha whose cross found Augusto Fernandez who headed into the bottom left-hand corner of the goal.
Half-time arrived without further score or any clear chances for either side.
Armenteros' drilled effort was held by Rodriguez Yoel but the match entered its final quarter with little impetus.
Krohn-Delhi fired over the bar, seemingly triggering some attacking intent in his team-mates.
Manuel Agudo Nolito's curling 20-yard shot was tipped round the post by Andres Fernandez before Alex Lopez's free-kick found the head of Santi Mina only for Fernandez to tip the ball over.
The Osasuna keeper then punched clear Nolito's free-kick before his opposite number Yoel was called upon to parry Francisco Punal's 25-yard free-kick.