The 35-year-old let fly first time from Sabin Merino's knockdown to beat Steve Mandanda with an audacious effort in the 54th minute.
Aduriz's strike stunned their Ligue 1 opponents, who have now won just one of their last eight games in front of their home fans in all competitions.
A goal of Aduriz's quality did not look likely during a dull first half.
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Visiting left-back Mikel Balenziaga scuffed a clearance straight to Mauricio Isla, who teed up Steven Fletcher on the edge of the area - but the Scotland international's goalbound effort was blocked by Oscar De Marcos.
The closest Athletic they came to to troubling Mandanda in the first half was when a corner was cleared to Javier Eraso on the edge of the area and the midfielder's first-time shot flew over the crossbar.
Athletic started the second half well, with Inaki Williams getting on the end of a long ball down the right before dragging a shot wide of the far post.
Nine minutes into the second half Athletic took the lead. After Merino got his head to goalkeeper Iago Herrerin's clearance, the ball dropped to Aduriz, who unleashed a brilliant volley that fizzed over Mandana and into the net.
Marseille pressed for a leveller but were unrewarded as Fletcher headed over and Florent Thauvin's deflected shot clipped the outside of the post, and must now head to Spain next week looking to overturn a first-leg deficit.
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