Griezmann gave the San Sebastian side the lead after 11 minutes after a quick break from the visitors saw Carlos Vela release the 21-year-old, who hit a left-footed shot past goalkeeper Roberto Gago.
Hector Litri was then sent off for the home side after receiving two yellow cards before the 25-minute mark.
The sending off meant that Sociedad have played against 10 men at some point in each of their last seven games and the visitors made their numerical advantage count when Aggiretxe added a second just after the half-hour mark.
The striker hit a right-footed drive low into the corner of Gago's right-hand corner following a corner.
Aggiretxe should have made it 3-0 just before the hour mark, but his free header went wide of Gago's left-hand post.
The third minute of injury time saw Apono dispatch a penalty to give the hosts a consolation for their efforts.