The former Valencia forward scored a trademark header with seven minutes to play to give his side an important point in their battle for fourth.
Aduriz missed the chance to give the visitors an early lead after Slovenia defender Bojan Jokic conceded a penalty in the 31st minute, as Sergio Asenjo denied the forward.
And Tomas Pina made Bilbao pay when he put Villarreal in front just two minutes into the second half.
Atletico Madrid loanee Oliver Torres created the opener, beating Mikel Balenziaga before playing an excellent ball across the face of the goal that Pina converted at the far post.
The game would have more twists in it though, as Brazilian Gabriel Paulista was sent off for a second yellow card with 25 minutes to play.
And Villarreal, conceding a numerical advantage, also lost their lead as Aduriz netted his 11th La Liga goal of the season.
The striker headed in Ander Iturraspe's cross, reading the flight of the ball better than Villarreal defender Aleksandar Pantic and powering his effort beyond Asenjo.
Bilbao are now six points clear of the fifth-placed Real Sociedad in the race for the fourth and final UEFA Champions League spot, while Villarreal remain sixth after the draw.
