The hosts very nearly took the lead after just three minutes as hesitation among the Leicester defence allowed Jose Izquierdo to race forward, but his ensuing shot flew wide of Kasper Schmeichel's goal.
It proved to be a seminal moment in the game as the Foxes ended up drawing first blood in the sixth minute, courtesy of a mishap at the back from Brugge.
A long Luis Hernandez throw-in led to Hans Vanaken flicking a header out of goalkeeper Ludovic Butelle's hands, and Marc Albrighton was on hand to bundle home his side's first ever Champions League goal.
Once again, Leicester punished their opponents as Riyad Mahrez curled a free kick over the wall and into the top-left corner of the net to take a two-goal lead into the break.
Michel Preud'homme's charges did not shore up their defence after the restart and, just before the hour, Butelle clattered into Vardy to gift the Foxes a penalty, which Mahrez coolly slotted down the middle.
It was only after conceding their third goal that the Belgian champions began taking their opponents to the sword, with Izquierdo charging into the Leicester box and sending a shot crashing against the bar in the 65th minute.
However, Claudio Ranieri's side did not let their heads drop, remaining tight at the back and sending waves of attacks forward in a bid to add to their goal tally.
The final whistle put an end to Brugge's misery, while the Leicester players, staff and fans were able to bask in the aura of a historic win that puts them top of Group G.