The Belgian side are guaranteed to progress from Group B after keeping Diego Simeone’s side at bay in Madrid, and finished the game with 10 men after Kamal Sowah was sent off in the final stages.
Brugge stunned Atletico last week at home with a 2-0 win and although they dropped their first points of the competition at the Metropolitano, still secured qualification for the knock-out rounds.
Goalkeeper Simon Mignolet made a series of impressive saves to deny the likes of Antoine Griezmann and Angel Correa, frustrating the Spanish side, who are on four points from four games, six behind Group C leaders Brugge.
The visitors had the better of the opening stages, with Ferran Jutgla, who shone last week against Atletico, going close.
However Simeone’s side wrestled their way into the game and Mignolet denied Griezmann at the other end.
Saul Niguez had a goal ruled out for offside against Correa in the build-up, and the Argentine soon fired narrowly wide himself, as Atletico began to dominate.
Brugge thought they had earned a penalty at the end of the first half but the decision was overturned by VAR, with Tajon Buchanan appearing to step on Nahuel Molina, rather than the reverse.
Correa struck shortly after the interval but he was offside too and it was stricken from the records. Brugge’s task of holding on for the point was made harder in the final stages when Sowah was shown a second yellow card for kicking the ball away.
Correa might have won Atletico the game at the death but Mignolet made another fine save to deny him.
Bayer Leverkusen host Porto in the other Group B game later Wednesday.
