Goals either side of half time from strike partners Kamal Sowah and Ferran Jutgla helped Carl Hoefkens's side become the first Belgium club in Champions League history to win their opening three group games.
Blauw-Zwart, wo were initially regarded as the outsiders of Group B, are now sitting top of the pile with a maximum of nine points, six clear of Atletico who sit rock bottom on goal difference at the halfway stage.
Club Brugge had only won one of their previous 18 European meetings against Spanish opposition prior to tonight's encounter against Atletico, but the underdogs prevailed in impressive fashion to edge themselves one step close to reaching the knockout rounds for the first time in their history.
While Atletico dominated proceedings for large spells of the match in Belgium, recording a total of 20 shots on goal, Brugge were clinical in the final third, with both Jutgla and Sowah in particular starring for the hosts.
Jutgla set up Sowah to break the deadlock in the 36th minute, weaving his way into the penalty box before rolling the ball across the face of goal for the latter to tap in from just a yard out.
Jutgla then scored one of his own, doubling Brugge's lead just after the hour mark, with the former Barcelona youngster guiding a sweet strike beyond a hapless Jan Oblak into the bottom-right corner.
Antoine Griezmann, who was starting only his second game of the season, had the chance to pull one back from the penalty spot after Matheus Cunha was brought down in the 75th minute by a challenge from Casper Nielsen, but the Frenchman smacked the ball onto the face of the crossbar and Brugge eventually cleared their lines.
Brugge held on for a historic win in front of their own fans, and they now sit six points clear of the remaining three teams in Group B, including Porto who secured their first win of this season's Champions League campaign after beating Bayer Leverkusen 2-0 in Lisbon.
Hoefkens's men will book their place in the last 16 of the Champions League for the very first time if they avoid defeat against Atletico when they lock horns for a second time at the Wanda Metropolitano next Wednesday.