Aduriz scored in the 15th and 45th minutes, powering the visitors to a comfortable half-time lead on the road.
Levante were much stronger in the second half, pulling a goal after the hour mark when Athletic defender Mikel San Jose put the ball in his own net, but the visitors held on for the three points.
Athletic moved to 59 points for the season and remain in fourth spot, which comes with a berth in the qualifying rounds of next season's UEFA Champions League, six points clear of fifth-placed Sevilla.
The Basque club did not have to wait much longer to open the scoring, however, with Markel Susaeta cutting the ball back to Aduriz and the striker's shot deflected wickedly off Levante's Victor, leaving goalkeeper Keylor Navas stranded.
Aduriz's second goal came in the shadows of half-time, as the 33-year-old notched his 13th of the season with a header from Ander Herrera's cross.
Levante were unable to find an equaliser, however, with Athletic going closest to scoring the fourth goal of the game when Muniain's close-range header was saved by Navas.
With games against Sevilla and sixth-placed Real Sociedad to come in the final six rounds of the Spanish league season, Athletic's fate in terms of Champions League qualification remains in their own hands and they have a significant advantage after Monday's win.
Barral backed into Estrada to simulate what had happened, knocking the ball out of the referee's hands, earning the 30-year-old a second yellow card.
