Enrique de Lucas had the first effort on goal for Celta Vigo after seven minutes, but his shot didn't trouble the goalkeeper.
A minute later, Osasuna hit back through a header from Lolo, but his attempt was cleared.
Nano broke free for the home side on 19 minutes, but he couldn't find the finish to give Osasuna the lead.
Emiliano Armenteros almost gave Osasuna the lead, hitting the bar with a header on 25 minutes.
Armenteros had another effort just before the half-time whistle, but he dragged his shot wide of the mark.
Osasuna took the lead on 55 minutes through Armenteros, who finished well to make it 1-0.
Park Chu-Young had a golden opportunity to grab the equaliser for the away side, but his hesitation allowed the defence to close him down.