The Belgian side took the lead when Thomas Meunier rifled home from a corner and it was 2-0 when Joseph Akpala side-footed past Colin Doyle.
Jean Beausejour pulled a goal back in the second half after Brugge failed to clear Nikola Zigic's effort.
And the point was secured by substitute Marlon King from the penalty spot after Ryan Donk fouled Beausejour.
Despite finding themselves 2-0 down at the break things could have been so different for Chris Hughton's side, who hit the woodwork twice.
David Murphy was first to rattle the frame before Guirane N'Daw saw a long range effort tipped on to the post.
The point leaves the Blues second in the Group H table, on head-to-head, with two games to play, and a real chance of qualifying for the knockout stages.
They started slowly and struggled to keep possession but in the end were the side who looked most likely to score a winner.
Two early chances for the visitors saw Vadis Odjidja in the thick of the action, his first effort a free-kick curled over the bar before he shot wide of the right-hand post.
Birmingham's first real opportunity came on 25 minutes when Jannes Vansteenkiste handled on the edge of the area under pressure from Zigic.
Murphy stepped up but his curling effort hit the crossbar, and Brugge took advantage of their reprieve by opening the scoring on 40 minutes.
A corner from Victor Vazquez found Meunier unmarked in the box and the striker took the ball down on his chest before guiding his finish past Blues midfielder Wade Elliott on the line.
And just before the break the visitors doubled their lead, Beausejour conceding possession and Vazquez finding Odjidja, who unselfishly squared from the right for Akpala to side-foot home.
Birmingham were back in it on 54 minutes as Elliott crossed for Zigic to control with his chest and after the 6ft 7in Serb's effort was blocked, the ball fell kindly for Beausejour to score his first of the season.
Seconds later Brugge should have restored their two-goal advantage as Odjidja's 25-yard shot beat keeper Colin Doyle, only for the post to intervene.
The woodwork rescued the visitors again on 71 minutes, with Kujovic tipping a long-range effort by N'Daw on to the post.
But Birmingham continued to press and got their reward two minutes later when they were awarded a penalty after Ryan Donk fouled Beausejour.
King stepped up and made no mistake, sending the keeper the wrong way to secure a point.
Birmingham boss Chris Hughton: "What we needed to do was give our fans something to cheer about and we were able to do that in the second half.
"These nights are an opportunity for our players to experience different types of challenges. Club Brugge were very expansive and have some really good footballers. Tactically they really tested us.
"This is a great experience for the club and the supporters, who are enjoying every minute of this.
"Our championship form is the biggest priority, we want to be fighting in the division but we can enjoy the Europa League. The fact we have done OK makes it a little bit better."