Aduriz converted from the spot in the second minute of added time after Girona goalkeeper Gorka Iraizoz had pulled off a string of outstanding saves to keep Athletic at bay.
Iraizoz was at full stretch to deny Inaki Williams and Aduriz early on, while Inigo Cordoba was thwarted in similar fashion.
Girona had a goal ruled out when the video assistant referee showed former Middlesbrough striker Cristhian Stuani had handled before turning the ball home in the 19th minute.
Athletic continued to chase the opening goal in the second period, but Iraizoz kept out another Aduriz effort and a low shot from Raul Garcia.
Iraizoz then saved headers from Aduriz and Unai Nunez in quick succession as Athletic maintained the pressure with 16 minutes left.
Girona appeared to have held on, but in stoppage time Jonas Ramalho fouled Iker Muniain in the area and Aduriz converted from the spot to secure Athletic a much-needed win.