Club record signing Falcao opened the scoring from the penalty spot in the third minute and, after Adrian Lopez had doubled Atletico's lead just after half-time, the Colombia international completed his treble with two more goals late on.
The victory ended Atletico's miserable away run and continued the impressive start made under new coach Diego Simeone, whose first three games in charge have now yielded seven points, with seven goals scored and none conceded.
Sociedad were also in good league form coming into the game having gone seven matches unbeaten to climb away from the relegation zone, but they were swept aside by Atletico.
Falcao was again the star of the show as he took his league tally to 14 goal for the season - almost exactly half Atletico's overall tally.
He broke the deadlock from the spot, sending Claudio Bravo the wrong way after Diego's attempted cross had struck the hands of Sociedad defender Vadim Demidov.
Atletico had chances to increase their lead before the break but a lack of control from Falcao and a poor mis-kick from Adrian let Sociedad off the hook.
The home side's main threat looked to be from free-kicks but they created little to worry Thibaut Courtois in the visiting net and Atletico made it 2-0 in the 46th minute.
Falcao was also involved in that goal, playing a slick one-two with Juanfran, whose cross to Adrian at the far post was slammed home at the second attempt after the striker's initial header was superbly saved by Bravo.
With Sociedad still struggling to break down the Atletico defence, the away side killed the game off as a contest in the 83rd minute with a brilliant finish from Falcao to make it 3-0.
Bravo had only ventured to the edge of his six-yard box but Falcao still managed to find the back of the net with a perfect chip from 25 yards out to the right of the area.
There was still time after that for the 40million euros summer signing from Porto to complete his treble, the goal coming in the first minute of stoppage time following a fine Atletico move.
Jorge Koke was at the heart of the attack, first cleverly dummying the ball before racing onto a through-pass that gave him time to pick out Falcao in the middle, and the 25-year-old South American coolly side-footed his volley past Bravo from 10 yards out.