Diego Simeone's side made an aggressive start and after spurning a few early chances they deservedly went ahead with a low finish from Yannick Carrasco in the 16th minute, doubling their lead in the 28th through Argentine forward Angel Correa.
After the match, Atleti's Koke said: "We're tired. We did a spectacular job today from beginning to end, at 2-0 we took a little step back at the end, but we made a huge effort to win, which is what we had to do beyond the good moments and not so good moments we had.
"This is about getting the three points, and on Sunday we have another game."
They finally got a goal when defender Igor Zubeldia bundled the ball into the net in the 83rd minute, ensuring a nerve-shredding finish for the leaders.
Atletico were hemmed into their own half for most of the remaining minutes but clung on for the victory and know they will lift a first La Liga crown since 2014 if they beat Osasuna and Real Valladolid in their final two fixtures.
"We have two games left, that's a whole world," Koke added. "The league is really tight these last five games, we've always said it. Everyone is dropping points, these games are finals for us, we won this one and on Sunday and we have another final we want to win.
"We're Atleti, if we weren't suffering, it wouldn't be us. Thanks to the fans who came here outside [the stadium] and those who can't. You need your fans to make that extra effort as we did in the last 10 minutes, we could hear them outside. We're grateful."
Atletico had earned a crucial draw away to Barcelona on Saturday but the point felt like little after a spirited, ambitious performance at the Camp Nou and the result handed the advantage in the title race to Real.
Yet the champions' 2-2 draw against Sevilla on Sunday meant Atletico's fate was back in their own hands and from the start they went all out for the win, ceding possession to the Basques but eating up the territory with an aggressive pressing game.
Marcos Llorente missed the first clear chance of the game with a bursting run through the middle but was thwarted by Sociedad keeper Alex Remiro after opting to shoot rather than pass to an unmarked Luis Suarez.
Llorente had a hand in the opening goal, playing a one-two into Carrasco, who slotted between the legs of Remiro.
Atletico are often happy to sit on a one-goal lead but did no such thing after going ahead and struck again when Suarez barged his way towards the area and released Correa, who slotted into the bottom far corner.
They conceded their fair share of chances but were able to count on the ever-reliable Oblak and looked to be in control until Zubeldia's late goal caused a nervous finale.
Yet they defended resolutely in the final minutes and Simeone punched the air as he raced down the tunnel at full-time.