The Belgian side have won their three opening games without conceding a goal and dominated Diego Simeone's side for much of the game, triumphing thanks to Kamal Sowah and Ferran Jutgla's strikes.
Antoine Griezmann, given a rare start, missed a second-half penalty for Atletico, who are level with Porto and Bayer Leverkusen on three points each, after the German side lost 2-0 in Portugal.
Alvaro Morata should have sent Atletico ahead after breaking into the box but former Liverpool goalkeeper Simon Mignolet saved his low strike after a tight opening spell.
Atletico coach Diego Simeone withdrew Marcos Llorente injured and more bad news quickly followed. Sowah fired the hosts ahead in the 36th minute from former Barcelona forward Jutgla's cut-back across the face of the goal.
Brugge should have doubled their lead at the start of the second half but Jan Oblak made a fine save to deny Jutgla, after fine work by Canadian Tajon Buchanan, with Atletico's defence sleeping on the job.
Yannick Carrasco lashed an effort well wide and Griezmann sent a shot into the side-netting as the visitors reacted to the wake-up call.
However, the effervescent Buchanan teed up Jutgla to finish with aplomb in the 62nd minute. The 23-year-old striker is in a rich vein of form – this was his eighth goal in 11 games across all competitions.
Griezmann crashed a penalty off the crossbar after Matheus Cunha was felled in the box, then had a goal ruled out for offside as Atletico's frustration grew.
Mignolet beat away Joao Felix and Angel Correa's efforts in the final stages to secure a noteworthy victory for his team and leave the 2014 and 2016 runners-up with a lot of work to do.