Marcelino's men are chasing a UEFA Champions League place and closed the gap on Bilbao, who drew 1-1 against Real Madrid on Sunday, to three points in La Liga.
Jeremy Perbet and Manu Trigueros struck in a nine-minute spell just after half-time before the former completed his brace.
Oriol Riera netted a stunning consolation for Osasuna three minutes from full-time as they stayed just two points clear of the relegation zone.
The hosts needed until the 47th minute to open the scoring through Perbet.
The French striker, who came on just before half-time, got on the end of a wonderful long pass from Jose Antonio Dorado to poke past goalkeeper Andres Fernandez.
Trigueros doubled the lead on 55 minutes when he picked up a Giovani dos Santos pass and drilled an effort into the bottom corner from 25 yards despite Fernandez getting a hand on the shot.
A well-worked move from a throw-in lead to the sealer 15 minutes from time as Jonathan Pereira played in Perbet, who volleyed past Fernandez.
Osasuna scored a consolation goal in the 87th minute, but Riera's effort was undoubtedly the pick of the goals.
Riera beat his marker to Emiliano Armenteros' cross and watched his back-heel float in off high off the back post.
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