Sociedad coach Imanol Alguacil said his side deserved the victory, but was not interested in discussing whether they could remain among the top three come the end of the season.
"These three points are important to us but so is every victory in this league, where any team can beat anyone else. We beat a side who were ahead of us and who're very strong at home and that says a lot of our players," he said.
"The league table doesn't mean anything to us, we're more interested in the way we play and we're very happy with how we played today," added Alguaci.
Granada coach Diego Martinez was proud of his team's performance but frustrated at the manner in which they lost.
"It's a real pity, the game was very evenly matched and I give my players 10 out of 10 for effort but it wasn't meant to be," said Martinez.
Granada play Valencia away next week while Real Sociedad host Leganes in the opening game of the weekend.
Osasuna on the move
Earlier, Osasuna continued their remarkable home form by beating Alaves 4-2 for a club record 31st home victory in a row in league competition.
The Pamplona club are in good form this season, having held champions Barcelona to a 2-2 draw as well as beating Valencia 3-1.