Mario Mandzukic also hit a brace as Atletico Madrid kept on their trail with a 3-1 victory in dismal weather at Eibar.
Champions Atletico are now level on 47 points with second-placed Barcelona, who face Villarreal on Sunday. Real have 51.
Real coach Carlo Ancelotti had high praise for his match winner Benzema.
"Benzema had a fantastic game as did all the forwards," said Ancelotti.
"The second goal he scored was excellent. You have to also value him for his all-round play and the way he helps the team. He is not just a goalscorer."
Real had to come from behind after being caught out inside the first minute with Aritz Elustondo heading visitors Sociedad in front.
But the league leaders, missing the suspended Cristiano Ronaldo, quickly equalised with James Rodriguez nodding in a Marcelo cross.
Sergio Ramos gave Real the lead in the 37th minute by smashing home a rebound after a Benzema shot had been saved by keeper Geronimo Rulli.
The game opened up for Real after the break and Benzema combined with Gareth Bale to slot in his first before curling a sweet effort into the top corner 15 minutes from the end.
"Since the start of the year we haven't been at our best but it is better to happen now than at the end of the season," Ramos told reporters.
Asier Illarramendi was a given a rare chance in midfield and Isco returned after injury, while Bale moved over to the left to cover for the absence of Ronaldo.
Sociedad coach David Moyes admitted Real were superior. "We started well but you can see the difference between the teams," he told a news conference.
Atletico's Antoine Griezmann maintained his strong form as he fired home the opener after seven minutes. The pitch looked more like a quagmire in parts as a result of heavy rain but Atletico adapted well and the combative Mandzukic knocked in a Griezmann cross from the left wing to make it 2-0 in the 23rd minute.
Then two minutes later he seized on a loose ball in the area and drove it past keeper Xabier Irureta. Federico Piovaccari headed in an 89th minute consolation for Eibar.
(Editing by Pritha Sarkar/Alan Baldwin/Ian Chadband)
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