And the hosts doubled their advantage soon after when Angel Correa found the far corner of the net with a composed finish after being played through on goal by the influential Llorente.
Real Sociedad were forced to withdraw Alexander Isak at half-time, but still posed a threat in the second half. However, Jan Oblak kept the visitors out as Atletico Madrid looked set to see out the win with relative ease.
A late goal from substitute Igor Zubeldia gave Real Sociedad a lifeline, with Atleti showing some nerves towards the end of the match. However, Simeone and his players did enough to secure all three points as fans celebrated outside the stadium.
The result moves Atletico Madrid four points clear of Barcelona at the top of La Liga and five points clear of Real Madrid, who will play their game in-hand against Granada on Thursday night.
TALKING POINT - Luis Suarez still hasn’t found his scoring touch after injury
The return of Luis Suarez from injury has given Atletico Madrid some much-needed energy and purpose in attack when they have needed it most in this title race, but the Uruguayan still hasn’t rediscovered his scoring touch. Time and time again, the 34-year-old was played in behind the Real Sociedad defence, but he spurned every opportunity. Suarez could have made this match much more comfortable for Atleti had he managed to keep his composure in front of goal.
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MAN OF THE MATCH - Yannick Carrasco (Atletico Madrid)
He was the standout performer for Atletico Madrid against Barcelona on Saturday and Carrasco was once again their best player here. The Belgian has been a key figure for Atleti this season, giving them a genuine threat out wide. Carrasco has been predominantly used as a wing back, but Simeone has moved him slightly further forward recently, putting the 27-year-old closer to goal. That paid dividends as Carrasco sent Atletico Madrid on their way with a crucial opener.
Atletico Madrid - Oblak 9, Hermoso 6, Felipe 6, Savic 5, Trippier 5, Carrasco 9, Saul 6, Koke 8, Llorente 8, Correa 7, Suarez 5. Subs - Kondogbia 5, Lodi 4, Felix 4.
16’ GOAL! Atletico Madrid 1-0 Real Sociedad: A huge goal for Atletico Madrid! It's Carrasco! The Belgian controlled a diagonal pass to the back post and squeezed a shot underneath Remiro into the back of the net! Carrasco has been in excellent form for Atleti!
28’ GOAL! Atletico Madrid 2-0 Real Sociedad: A second goal! Atletico Madrid have a two-goal cushion and it's Correa who has found the bottom corner of the net! Suarez played the ball through and Correa showed great composure to tuck the finish past Remiro!
37’ Against the post! Isak bundled his way through the Atletico Madrid defence and unleashed the shot, but Oblak tipped the ball on to his near post! That was very, very close!
80’ Off the post! Inches away from being a lifeline in this game for Real Sociedad! Portu was released through on goal, but he could only hit the base of the far post! And he couldn't stick away the rebound!
83’ GOAL! Atletico Madrid 2-1 Real Sociedad: A lifeline for Real Sociedad and it's game on at the Wanda Metropolitano! Atletico Madrid didn't deal well with the corner kick into the box, it bounced around a bit and Zubeldia was on hand to slam home the finish on the stretch!
No player has provided more assists in La Liga this season than Marcos Llorente (11), who has also scored 12 goals.
Angel Correa has had a direct involvement in 19 goals (in all competitions) for Atletico Madrid this season, his most productive season for the club.