Aduriz ended a run of five games without a goal to see off the challenge of Malaga, as his strike two minutes into the second half secured the Copa del Rey quarter-final 1-0 on aggregate.
After the first leg in Malaga finished scoreless on January 21, Bilbao dominated their home leg, taking 10 shots to four, with Aduriz providing the crucial moment in the 48th minute.
A counter-attack saw the ball spread right to Markel Susaeta, who squared a pass to Aduriz at the top of the six-yard box and the 33-year-old striker finished into the bottom corner of the net.
The win was Bilbao first in six games in all competitions, while Malaga's winless run stretched to six matches.
In Sevilla, the home side won 1-0 but were unable to overcome Espanyol, who triumphed 3-2 on aggregate.
Diogo Figueiras struck a brilliant curled shot over Espanyol goalkeeper Pau Lopez in the 88th minute at Sevilla's Estadio Ramon Sanchez Pizjuan but the home side were unable to find another goal in the remaining minutes to progress on the away-goals rule.
Villarreal joined Espanyol, Bilbao and Barcelona in the semi-finals with Gerard Moreno scoring in the 78th minute away to Getafe to complete a 2-0 aggregate triumph.
