Mauricio Pochettino started with his formidable attacking trio at Jan Breydel Stadion on Wednesday, with Mbappe teeing up Ander Herrera for the opener after a mazy run on the left flank.
Many may have expected Brugge to crumble, however, they responded through Hans Vanaken's fifth goal in eight games in the competition.
Mbappe was forced off in the second half with a slight foot problem as PSG, despite its embarrassment of attacking riches, failed to kick-off their Group A campaign with a win.
The visitor started brightly, Mbappe dancing past Clinton Mata before finding Herrera, who opened the scoring after 15 minutes with a first-time left-footed strike into the bottom-left corner.
Mbappe should have added a goal of his own after being rolled through by Messi but his right-footed drive was beaten away by Simon Mignolet.
Brugge then stunned the star-studded away side, with Eduard Sobol driving down the left flank before cutting back to the penalty spot, where Vanaken powered past Keylor Navas for his seventh goal in the Champions League - the most in his club's history.
Messi looked to respond immediately but his left-footed strike smashed against the crossbar before Vanaken and Charles de Ketelaere were both denied by smart Navas saves.
Brugge almost took the lead after the break through Jack Hendry but Presnel Kimpembe produced an important last-ditch block, with Mbappe limping off moments later following a challenge from Stanley N'Soki.
Noa Lang acrobatically volleyed wide in another fright for PSG before substitute Nuno Mendes found Messi, who spurned a glorious opportunity to win the game as he blasted over.