The game-defining moment came just a few minutes into the second half, when Mings picked the ball up in the area, seemingly unaware that goalkeeper Emiliano Martinez had already taken his goal kick.
Referee Tobias Stieler was left with no option but to point to the spot, and the experienced Hans Vanaken stood up and converted from 12 yards to put the hosts in front.
Apart from that extraordinary sequence of events, there was little to separate the two sides on the night in a low-key affair that produced very few clear-cut opportunities.
Ollie Watkins went closest for Unai Emery's side midway through the first half, flashing an effort just wide of the post, before Ferran Jutgla and Christos Tzolis were denied by a combination of post and Martinez for the home side in the space of 10 seconds shortly after.
Villa were seemingly taken aback after going behind, and struggled to get a proper footing in the game, with Brugge the only side looking threatening, as Andreas Skov Olsen and substitute Bjorn Meijer both squandered good opportunities with roughly a quarter of an hour to play.
Despite making numerous subs late on, Emery's men were unable to break down a stubborn Brugge rearguard late on, as the game finished 1-0 to the hosts.
The result leaves Villa fifth ahead of the 8pm kickoffs on Wednesday night, while Brugge move up into the top 24 and onto six points from four games.
CLUB BRUGGE VS. ASTON VILLA HIGHLIGHTS
Vanaken penalty vs. Aston Villa (52nd min, Club Brugge 1-0 Aston Villa)
It is a disastrous moment for Mings on his Champions League debut, as a complete loss of concentration sees him inadvertently pick the ball up in the penalty area after Martinez's goal kick, leaving referee Stieler with no choice but to point to the spot. Vanaken steps up and fires down the middle to give the hosts the lead early in the second half.
MAN OF THE MATCH - HANS VANAKEN
Brugge fans may jokingly offer this award to Mings after his horror show surrounding the penalty incident, but in a game that lacked a cutting edge for large periods, Vanaken takes it for showing the composure from the spot to win all three points for Nicky Hayen's side
CLUB BRUGGE VS. ASTON VILLA MATCH STATS
Possession: Club Brugge 44% - 56% Aston Villa
Shots: Club Brugge 13 - 8 Aston Villa
Shots on target: Club Brugge 7 - 1 Aston Villa
Corners: Club Brugge 2 - 3 Aston Villa
Fouls: Club Brugge 12 - 12 Aston Villa
BEST STATS
WHAT NEXT?
After four games without a win, Villa face another uphill task when they travel to Anfield to face Premier League leaders Liverpool on Saturday night, while Brugge will be expectant of three valuable points when they face Beerschot on the road 24 hours later.