David Zurutuza crashed in a volley from inside the area following a corner to put the visitors ahead in the 16th minute but Athletic responded superby.
Only four inspired saves from Geronimo Rulli prevented an equaliser before halftime but a wonderful individual goal from Iker Muniain deservedly pulled Athletic level in the 51st minute.
The forward cut inside from the left to hook the ball into the far corner and within 10 minutes, Aritz Aduriz had put Athletic in charge with a cool chip over the stranded Rulli after a mix-up between the goalkeeper and defender Raul Navas.
Then the veteran striker Aduriz pounced on more woeful defending to lay on the pass for Inaki Williams to knock in the third in the 72nd minute.
A well-worked set piece saw Sociedad defender Inigo Martinez head home in the 83rd minute to set up an exciting finish, but Athletic held firm to move up to fifth in La Liga.
Earlier, Alaves were denied a third win of the season as a late missile from Roberto Rosales saw them draw 1-1 at home to Malaga in a feisty game that ended with each side having a player sent off.
Brazilian striker Deyverson had put Alaves in front in the eighth minute and had a goal ruled out for offside, correctly, in the 89th minute.
Alaves defender Theo Hernandez was given a straight red card a minute later for a dangerous challenge, while Malaga substitute Juanpi was shown a second yellow card for dissent in the 93rd.
Valencia visit Sporting Gijon later on Sunday in new coach Cesare Prandelli's first game in charge and Villarreal host Celta Vigo.