Goals from Jeremy Perbet (22), Javier Aquino (30) and Ikechukwu Uche (75) made it three wins from three for the Yellow Submarine to lift the top-flight newcomers to the top of the standings.
Osasuna, however, are already bracing themselves for another tough campaign having lost all of their fixtures so far.
Marc Valiente's second-half header was enough to seal Real Valladolid's first win of the season at home to Getafe.
Valiente connected with Omar Ramos' headed on cross just after the break to seal a 1-0 win.
Rafinha Alcantara and Piti both scored their first goals for their new clubs as Celta Vigo and Granada shared a 1-1 draw at Balaidos.
Rafinha, the brother of Bayern Munich midfielder Thiago who is on loan from Barcelona, broke the deadlock with just under half an hour gone.
Piti, who joined Granada on a free transfer from Rayo Vallecano, where he was the top scorer last season, levelled after 60 minutes.
Saturday's La Liga Results