Chris Hughton’s side trailed 2-0 at the interval with Thomas Meunier and Joseph Akpala striking in a five-minute spell just before the interval.
But Jean Beausejour reduced the arrears and then won the penalty converted by substitute Marlon King which brought the Carling Cup holders level.
It means City, Brugge and Braga are all level on seven points with two games remaining.
Blues showed a tremendous fighting spirit with Beausejour coming alive and causing all sorts of problems in the second period.
Full-back David Murphy also got forward to good effect from left-back.
Brugge, roared on by their 3,000 fans, were the first to settle and Akpala got on the end of a cross from Thibaut van Acker but directed his header wide.
Akpala then timed his run to stay onside in running onto a chipped ball from Victor Vazquez. At full stretch he poked the ball past the post.
Blues threatened for the first time and Nikola Zigic appealed in vain for a penalty after being challenged by Jannes Vansteenkiste.
Akpala became the first player to be yellow-carded after 22 minutes for a challenge on Murphy. City were now in the ascendancy and came within inches of taking the lead after 26 minutes after Vansteenkiste handled on the edge of the Brugge box.
Murphy curled his free-kick past the defensive wall but it crashed against the angle of post and crossbar.
Zigic then climbed above the Brugge defence to meet a deep cross from Keith Fahey but he directed his far-post header wide.
After 39 minutes Meunier took advantage of poor marking to put Brugge in front. No one picked him up as he attacked Vazquez’s corner and he had time to take the ball down on his thigh before driving the ball past Blues goalkeeper Colin Doyle.
Five minutes later Akpala doubled Brugge’s lead after City were caught out by a quickfire counter-attack. He was left with a simple tap-in after Vazquez turned the ball across the six-yard box.
Zigic had a chance early in the second half to reduce the arrears but he failed to make a full contact on his attempted shot from a narrow angle.
The Serbian turned creator when teeing up a chance for Adam Rooney but his shot was blocked by Daan van Gijseghem.
Then after 54 minutes Beausejour gave the home side a lifeline with his first goal of the campaign.
Zigic controlled a cross from Wade Elliott and his shot was blocked but Beausejour was alert to the rebound and fired past Vladan Kujovic.
Brugge went straight down the other end and Vadis Odjija swept a curling shot against a post with Doyle stranded.
Zigic was causing problems but was booked for dissent after 57 minutes, before Kujovic was yellow-carded for time-wasting and Ryan Donk was cautioned for bringing down Rooney.
Murphy curled a free-kick just wide before Hughton made a treble change after 65 minutes with Zigic, Rooney and Elliott making way for King, Chris Burke and Chris Wood.
Kujovic produced a superb save to turn a 35 yard pile-driver from Guirane N’Daw onto the post.
But after 74 minutes St Andrew’s erupted when King levelled from the penalty spot after Donk was adjudged to have brought down Beausejour. N’Daw was booked before King sent Kujovic the wrong way from the spot.