Kike Sola put the hosts ahead on 28 minutes and Nino doubled the lead 15 minutes into the second half, leaving an impotent Deportivo with too much to do in the remaining half an hour.
The Galicians were second best for most of the game but came into life in the final 20 minutes, and a goal by Javier Camunas in the first minute of stoppage time made for a tense finish. However, Jose Luis Mendilibar's side held on for the three points.
It was the first defeat of Domingos Paciencia's brief reign in charge of Deportivo, which began with a win over Malaga and a draw with Real Sociedad. Yet none of the positive influence he had had on those two performances was evident against Osasuna, whose strong defence kept his side at bay.
A tight start to the game soon lead to Osasuna taking the initiative, with midfielder Alvaro Cejudo and winger Emiliano Armenteros creating openings in the Deportivo defence.
Kike Sola broke the deadlock midway through the first half when he acrobatically got on the end of a cross from Armenteros after a quick counterattack, but replays showed the Argentinean winger was offside when he put in the cross.
Deportivo could only manage one attempt on goal in the first half, a poor attempt at a lob by Riki that was easily saved by Osasuna goalkeeper Andres Fernandez.
The hosts doubled the lead on 60 minutes, when Lolo took a free-kick quickly, chipping the ball over the wall and into the path of Nino, who smashed his shot into the top corner.
It said a lot about Deportivo's weak attacking display that the first player to come closest to scoring for them was the Osasuna defender Alejandro Arribas, who diverted a cross from Pizzi narrowly over his own crossbar.
This chance seemed to galvanise the visitors, who then started to pressure their opponents. Substitute Nelson Oliveira had two great chances to pull one back, first when he fired a through ball by Ze Castro straight at Fernandez, and then failed to take advantage of a defensive slip by Ruben Gonzalez, and was again denied by the Osasuna goalkeeper.
Deportivo got the goal their pressure deserved when former Osasuna player Camunas poked home a Pizzi cross at the near post a minute into time added on, but by then it was too late.