David Villa and Koke scored either side of half-time to give Diego Simeone's side a two-goal lead, which was reduced by a late strike by Xabi Prieto.
Atletico goalkeeper Thibaut Courtois then had to make two stunning saves in the final moments of the game to preserve all three points.
Atletico fielded an unchanged side from the team that drew 0-0 with Barcelona but surrendered the Spanish Super Cup, on away goals on Wednesday, while Liassine Cadamuro replacing the injured Carlos Martinez was Real Sociedad coach Jagoba Arrasate's only change from the side that beat Lyon 2-0 at home in the second leg of their Champions League play-off tie.
Real Sociedad needed just three minutes to give their opponents an almighty scare, as Antoine Griezmann volleyed the ball into the ground and off the crossbar.
Carlos Vela then tried his luck from the edge of the area, but overhit his shot and watched it fly over the bar.
Villa came closer to scoring not long after, striking a cut-back from Koke just above the crossbar, and then took advantage of a poor pass from Inigo Martinez to shoot from the edge of the area, his effort striking the post.
The Spain striker was later denied by Real Sociedad goalkeeper Claudio Bravo, before finally breaking the deadlock with his fourth attempt on goal.
Villa played a one-two with Diego Costa but appeared to have lost possession to Ansotegi, before winning the ball back and dinking the ball over Bravo into the net, to score his first league goal of the season.
The hosts then dominated play in search of an equaliser, but could barely muster a chance, and found themselves two goals down within 10 minutes of the second half, the victim of a perfectly executed Atleti counter-attack.
Costa sent the ball towards Arda on the left wing and the Turkish international then played in Villa by the byline, who cut the ball back across the box with Koke diving to meet it with his right foot, sending the ball beyond Bravo.
Diego Costa later missed an opportunity to kill the game off, narrowly failing to connect with a Miranda header at the far post, and then Real Sociedad got themselves back in the game.
Prieto received the ball inside the area following a quickly taken free-kick and hit it first time into the opposite corner.
Sociedad then laid siege to the Atleti goal in the closing stages but were thwarted by two outstanding stops from Courtois within the space of a minute.
Esteban Granero fired a low shot towards the bottom corner but the Belgian somehow managed to get down and tip the ball over the bar.
A minute later he dove across goal to beat away a shot from Ruben Pardo that looked destined for the top corner and preserve three points for the visitors.