Sociedad, who were the surprise package of last season as they finished fourth in the table, defeated Getafe 2-0 at home thanks to goals in either half from Carlos Vela and Haris Seferovic.
Mexican Vela lobbed effort broke the deadlock just before the break, while Seferovic, making his debut for Sociedad following a summer move from Fiorentina, doubled the lead with 20 minutes remaining.
Sociedad were under the guidance of Jagoba Arrasate for the first time after he replaced Philippe Montanier this summer and it was a good day for another new coach in Ernesto Valverde, whose reign as Athletic coach also got off to a winning start with a 2-1 win at Real Valladolid.
Markel Susaeta gave the visitors the lead on 28 minutes, but just moments later Patrick Ebert levelled for Valladolid.
However, Athletic were not to be denied as Iker Muniain netted the winning goal in the 50th minute.
Valencia laboured to a 1-0 win at home to Malaga thanks to a second-half goalby Ricardo Costa.
The Portuguese centre-back took advantage of an error from Malaga stopper Willy Caballero to nudge the ball home after 64 minutes, giving his side a win they just about deserved.
Under new boss Bernd Schuster, Malaga started with just five players who were regulars last season, with the core of Manuel Pellegrini's side from 2012-13 having left the club in the summer.