The young New Zealand international, who is on loan from Premier League club West Bromwich Albion, scored his tenth goal in his last ten outings for Birmingham in the tenth minute of stoppage time to help his side complete a great fightback.
The match looked as though it was headed for a draw but the head injury to Birmingham's Pablo Ibanez, who was taken from the pitch on a spinal board, forced the game to ten minutes of added time and it was in the final minute that Wood slotted the winner at the neat post from Marlon King's cross from the right.
Birmingham have moved to equal top of Group H, sharing six points with Brugge, whilst Sporting Braga dropped to third following their 1-1 draw with bottom-placed NK Maribor.
Europa League Group H
Club Brugge (BEL): 1 (Joseph Akpala 3') Birmingham City (ENG): 2 (David Murphy 26', Chris Wood 90+10') Jan Breydel Stadium, Bruges Yellow cards:BRU - Jonathan Blondel 31', Niki Zimling 68' BIR - Nikola Zigic 35', Jonathan Spector 77', Wade Elliott 82'