With rivals Barcelona losing to Valencia 3-2 on Saturday, Atletico guaranteed their position as outright leaders ahead of Real Madrid's clash with Athletic Bilbao in the late Sunday game.
David Villa's close-range finish set them on their way in the first half before Diego Costa slotted home his 25th goal of the season with less than 20 minutes remaining.
Miranda headed in a first league goal soon after, and the returning Diego struck to cap an emotional night at Vicente Calderon, which saw players and fans pay tribute to legendary player and four-time coach Luis Aragones, who died on Saturday.
New signing Diego was on the bench as Atletico coach Diego Simeone made four changes from the Copa del Rey triumph at Athletic Bilbao in midweek.
Costa retained his place up front, and he almost opened the scoring with a lung-busting run that saw Claudio Bravo save acrobatically early on.
Atletico thought they had taken the lead when Koke's beautifully threaded pass found Villa, who rounded Bravo and slotted in, but the Spain international was marginally offside.
In Sociedad though, the hosts were up against a side who had won six of their previous eight league games, and they almost snatched the lead midway through the first half when Antoine Griezmann found space on the edge of the area only to see his drilled effort repelled by Thibaut Courtois.
Atletico edged ahead after 37 minutes following an incisive move that saw Costa cross for Villa to sweep home from close range, with the former Barcelona man pointing to the sky in tribute to Aragones during his celebration.
Sociedad responded well early in the second half and Ion Ansotegi fired narrowly wide when Atletico failed to clear a corner.
Diego was introduced as a substitute shortly after the break, and his neat cross found fellow replacement Raul Garcia who had sprung the Sociedad offside trap in the 67th minute, but he elected to head towards goal rather than controlling the ball and could not trouble Bravo.
Sociedad's offside trap failed again six minutes later and this time it proved decisive as Costa strode forward and coolly slotted beyond Bravo from 12 yards before Miranda added a third as he rose highest to power a header into the bottom corner.
Garcia almost added a fourth, but Bravo clawed away his bullet header, but a perfect night was rounded off three minutes from time when Diego showed great poise to control before smashing past Bravo as Atletico went top in style.
