The draw left Atletico on 70 points, 17 behind champions and city rivals Real Madrid and 12 behind Barcelona. They will be joined in next season's Champions League by fourth-placed Sevilla, who beat Valencia 1-0.
Granada hammered Atletico Bilbao 4-0 to nab seventh place and a spot in the second qualifying round of the Europa League.
Needing only a point to make it into Europe next season, Real Sociedad's dream was almost shattered when an outrageously brilliant backheel from Atleti's Alvaro Morata teed up the ball for Koke to blast home on the half-hour mark.
However, a free kick three minutes from time by Januzaj somehow flew into the net, thus securing Real Sociedad a place in Europe next season.
Roberto Soldado got Granada off the mark in the 29th minute and second-half goals from Antonio Puertas, Carlos Fernandez and Angel Montoro helped them breeze past Bilbao. They finished with 56 points.
Villarreal had already secured fifth place in the standings and qualification for the group stages of the Europa League, while Getafe slumped to a 1-0 defeat by Levante to miss out on Europe, finishing in eighth place on 54 points.