An early goal from Joseba Garmendia set the Basque side on their way in a dominant first-half display, although the outcome of the game remained in the balance until Fernando Llorente finally sealed the victory in the closing stages.
The result puts four points daylight between the two clubs with the Pamplona-based side still winless this season and rooted to the foot of the table with only five points from 11 matches.
Athletic set a fast tempo from the first whistle, putting Jose Antonio Camacho's men on the back foot with a flurry of long-range efforts and dangerous-looking crosses into the box.
Llorente, who was earlier named in the Spain squad, was central to most of their good work and he was clearly determined to celebrate his first international call-up with a goal against his hometown club.
The big striker was frustrated in most of his early attempts but his presence caused Osasuna all kinds of problems and it was his surging run into the box that created the breakthrough after 15 minutes.
Llorente collected a ball with his back to goal and burst between two defenders before the ball ran loose from a crowd of legs for Garmendia to slot into a virtually unguarded net from eight yards.
It was fair reward for Bilbao's bold endeavours and they continued to press in search of a second, Llorente hitting the post moments later with a glancing header from a corner.
Pablo Orbaiz then called Roberto into action and such was the extent of the hosts' dominance they would have been disappointed to head into the break with only a one-goal lead.
However, Osasuna came out in determined fashion after the interval and tried to take the game to their hosts, although they generally lacked the quality to make the most of some decent openings whenever they found their way into the Athletic box.
Cesar Cruchaga did bring a save out of Gorka Iraizoz with a header from a Nasoud Shojaei cross, but Krisztian Vadocz and Walter Pandiani should have both hit the target from good positions either side of that.
The Basques needed a lift to make sure their earlier work did not go to waste and Joaquin Capparos chose the moment to introduce veteran striker Joseba Etxeberria in place of Garmendia, immediately bringing the nervy San Mames crowd back to life.
Athletic got themselves a foothold back in the game and things opened up with both sides being bold in their attempts to find the all-important second goal of the game.
The visitors came close with a couple of set pieces as they threw caution to the wind in the final 10 minutes but it was Llorente who eventually settled matters with only two minutes remaining on the clock.
The big striker took a ball into feet following a succession of passes out on the right, showing strength to hold off Cruchaga before turning to stroke a shot across Roberto and into the far corner.