Llorente wins Basque derby for Bilbao
The Spain striker scored in each half to sink Sociedad and earn coach Marcelo Bielsa the first victory of his reign at the sixth time of asking.
Sociedad had levelled through defender Inigo Martinez's astonishing strike from his own half but were outplayed for the majority of the encounter and had no answer after Llorente's second.
The visitors were first to threaten as Markel Susaeta's effort was tipped around the post by goalkeeper Claudio Bravo and Javi Martinez headed over from the resulting corner.
Oscar De Marcos tried his luck from 30 yards but Bravo comfortably held his shot. Sociedad broke upfield but David Zurutuza's long-range strike was blocked by Carlos Gurpegi.
Iker Muniain drew another sharp save from Bravo but Llorente made the breakthrough when he slotted home from De Marcos' cross in the 34th minute.
Bilbao started slowly in the second period and Zurutuza shot over before Martinez drew them level shortly after the hour mark. Spotting visiting keeper Gorka Iraizoz off his line, the 20-year-old let fly from just beyond the halfway line to score a spectacular first goal of his career.
Llorente restores Bilbao lead
And his side could have taken the lead moments later when Antoine Griezmann shot against the post, but they soon fell behind and never looked like responding thereafter.
Llorente was the man to restore Bilbao's lead in the 70th minute, volleying home from inside the penalty area after being picked out by Fernando Amorebieta.
Andoni Iraola and Llorente tried their luck from 25 yards in a bid to kill the game off, but two goals proved sufficient for Bielsa to break his duck.