Athletic's new Argentine coach Marcelo Bielsa had been under pressure after the Basque club took only two points from their opening five games but a second consecutive win lifts them to 11th on eight points from seven matches.
Spain Under-21 international Muniain (pictured) put the home side ahead on the half hour at their imposing San Mames stadium, before Gabilondo and Martinez made it 3-0 before the break.
Osasuna's Iran midfielder Javad Nekounam pulled a goal back from the penalty spot in the first minute of second-half stoppage-time after Martinez handled the ball in the area.
The pair have a one-point advantage over third-placed Real Madrid, who thumped visiting Real Betis 4-1 on Saturday thanks to a third hat-trick in two weeks from Messi's Argentina team-mate Gonzalo Higuain.
