The result capped a remarkable comeback after the Blues had slipped a goal behind after just three minutes courtesy of Joseph Akpala's strike.
Working their way back into the contest, Chris Hughton's men equalised through David Murphy midway through the first half, and found a winner at the death as the substitute pairing of Wood and Marlon King linked up in style.
The result puts Birmingham level on points with Brugge at the top of Group H with two wins from three games, and following Maribor's 1-1 draw with Sporting Braga in the other group game, they have a real chance of reaching the knockout stage.
The only downside of an excellent evening's work for Birmingham came when Pablo Ibanez suffered a nasty injury late on after a clash of heads.
Fortunately Hughton was able to confirm after the match that the defender had only suffered concussion.
The Blues, making six changes from the side that beat Leicester 2-0 in the Championship at the weekend, started slowly and were punished immediately.
The group leaders went ahead after just three minutes, with the effervescent Nabil Dirar whipping in a low cross from the right that Nigerian striker Akpala tucked beyond Boaz Myhill.
And they spent the next 20 minutes in total control, going close again when Jannes Vansteenkiste headed into the side netting from a corner.
But the momentum changed when Birmingham scored against the run of play.
Chris Burke was afforded a touch too much room, and placed a teasing cross in, and Tom Hogli did not spot Murphy's late run to the far post, all the Blues' left-back to stroke the ball past Colin Coosemans in the Brugge goal.
From there Birmingham seized control, with Adam Rooney having two excellent chances to put the visitors ahead, only to miss the target on both occasions.
Brugge regrouped during the interval and came out an improved side in the second half, with the Moroccan midfielder Dirar firing an early warning shot from distance which Myhill saved.
Nikola Zigic had a gilt-edged chance to score Birmingham's second on the hour mark, but having got to Burke's cross ahead of the mismatched Hogli, he put his header wide of the far corner.
The Belgians had more of possession but struggled to fashion chances, and the game looked as if it was petering out into a draw.
The night was soured when Pablo and Akpala clashed going for a header in the penalty area in the final 10 minutes.
Pablo was stretchered off amid much concern, with Guirane N'daw moved to tears as he looked on.
That meant 10 minutes of stoppages, and after Wade Elliott fizzed a long-range shot close, King broke forward on the right hand side, squeezed a cross in where Wood was waiting to secure the Championship side another notable European scalp.