On the day Atletico saw its LaLiga crown taken by bitter rival Real Madrid, Diego Simeone's men started sluggishly and were duly punished inside 10 minutes when Mario Hermoso turned Inaki Williams's cross into his own net.
Williams, who was a constant threat, then sealed all three points in the 56th minute from the penalty spot.
Atletico remains in fourth place on the table, yet fifth-placed Real Betis can cut the gap to just a point if it overcomes Getafe on Tuesday (AEST). Athletic, meanwhile, remains in eighth.
Athletic's bright start was rewarded in the eighth minute when Hermoso deflected Williams's cross past Jan Oblak after the forward outmuscled Jose Gimenez.
Williams came agonisingly close to scoring for himself soon after, the 27-year-old's inswinging cross from the left missing everyone and bouncing off Oblak's left-hand post.
Geoffrey Kondogbia flashed wide as Atleti woke from their slumber shortly before the interval, while Yannick Carrasco saw an effort deflected just past Unai Simon's upright after a surging run.
Athletic doubled its advantage a few moments after Antoine Griezmann had thundered a free-kick against the crossbar, Williams clipping his spot-kick down the middle after Hector Herrera had brought down Iker Muniain just inside the area.
Muniain and Nico Williams were denied in quick succession by Oblak as Athletic looked to add further gloss to the scoreline, while Angel Correa saw an effort deflected against the post deep into stoppage-time for luckless Atletico.