The game failed to live up to its billing in a drab first 45 minutes, but Atleti broke the deadlock early in the second when defender Hermoso headed home a free kick from Yannick Carrasco.
The visitors added to their lead with a vicious strike from Llorente after a lay-off from Luis Suarez.
Real Sociedad were boosted by the return of playmaker David Silva from injury but struggled to create much danger and did not manage a shot on target until Atletico keeper Jan Oblak tipped a Martin Merquelanz free kick around the post late on.
Atleti, who recorded their 300th win in 499 games in all competitions under manager Diego Simeone, have 32 points from 13 games ahead of second-placed Real Madrid who have played 14 and host Granada on Wednesday.
"We knew how important this game was and what it would mean to win it and keep a clean sheet," said Hermoso.
"We keep fighting in every game, demanding so much of overselves and overcoming difficulties. It might look easy from the outside but it isn't."
Sociedad, who had led the standings for most of the season until their recent slide, slumped to a third straight league defeat and have now not won in their last nine matches in all competitions.
A victory would have seen them go level on points with Atletico but instead they trail Simeone's side by six and have played three games more.