The match at the Anoeta looked set to finish in a draw until Falcao stepped up in the 90th minute to strike home a 25-yard free-kick that left Sociedad goalkeeper Enaut Zubikarai grasping at thin air.
That was Falcao's 12th goal of the season in all competitions for Atletico and helped the Rojiblancos earn a sixth successive league victory that moved them back level on 22 points with Primera Division leaders Barcelona.
For Sociedad, the defeat ended their 100 per cent home record this season and left them three points above the relegation zone.
There were few chances for either side in the opening hour, although Sociedad felt they should have had a penalty on the stroke of half-time claiming Atletico midfielder Gabi had blocked a shot with his hands. Their appeals fell on deaf ears, though.
The match finally started to liven up around the 60-minute mark with Sociedad almost fashioned a clear chance following a rapid counter-attack.
Immediately after that attack was repelled, Atletico raced down the other end and twice came close to taking the lead.
Jorge Koke's well-struck shot from the edge of the box was parried by Enaut Zubikarai straight to Falcao 12 yards out, but the prolific Colombian could not find the back of the net with an acrobatic effort.
Soon after that miss Sociedad winger Antoine Griezmann opened up a shooting chance 20 yards out, but he could only fire straight at Thibaut Courtois in the visitors' goal.
The action swept back down the other end again where Atletico substitute Cristian Rodriguez drew a good diving stop out of Zubikarai, who four minutes later produced a stunning one-handed save to tip the ball over and avoid an own goal after his team-mate Mikel Gonzalez had flicked on an Atletico free-kick with his head.
With eight minutes to go Sociedad created a gilt-edged chance to take the lead when Carlos Vela was picked out in wide open space on the right.
However, after progressing into the area and with only Courtois to beat, the Mexico international sliced his right-footed shot horribly high and wide.
That proved to be a costly miss as eight minutes later Falcao found the back of the net with a dipping curling free-kick to give Atletico the points.