Atleti looked on course for victory in their concluding LaLiga fixture at the Wanda Metropolitano on Sunday after Koke's close-range finish in the first half.
But Januzaj's curling free-kick late on went through a crowded box and found a way past the otherwise superb Jan Oblak.
The point was enough for Atleti to claim third place in LaLiga but Sociedad were the happier of the two sides as they finished in sixth spot, when defeat would have left them without European football.
