Marc Albrighton capitalised on a goalkeeping error to fire the visitors ahead after just five minutes before Riyad Mahrez's sublime free-kick put the Foxes in control after half-an-hour.
And after Jamie Vardy was downed by goalkeeper on the hour, Mahrez netted his second of the night from 12-yards to secure an astoundingly simple three points for the English champions to open their European campaign.
It was their first win on a continental stage since 1961 and demonstrated plenty to suggest that Leicester are capable of reaching the knockout phase of the competition.
Leicester hand £30 million striker Slimani his debut
Claudio Ranieri made two changes from the Leicester side that crashed to a 4-1 defeat away at Liverpool in the league on Saturday.
Club-record signing Islam Slimani, brought in for £30 million from Sporting Lisbon on deadline day, replaced Shinji Okazaki to make his debut up-front alongside Jamie Vardy.
At right-back, Luis Hernandez replaced Danny Simpson after the Englishman was forced off at Anfield at the weekend suffering from tightness in his hamstring.
Club Brugge head coach Michel Preud'homme named four changes himself, from the team that fell to a 1-0 defeat at Waasland-Beveren on Saturday.
In defence, Boli Bolingoli and Benoit Poulain dropped to the bench in favour of Laurens De Bock and Bjorn Engels, while Tomas Pina came in for Claudemir in central midfield.
Up front, Jose Izquierdo return from a quad strain to lead the line while midfielder Timmy Simmons, who is the competition's oldest outfield player with just three months until he turns 40, captaining the home side.
Albrighton hands Foxes the lead after Izquierdo spurns early chance for hosts
Leicester, renowned for being such a stubborn defensive outfit last term, almost found themselves behind after just three minutes.
Colombian winger Izquierdo - Brugge's most dangerous attacking outlet - was sent through on goal by Hans Vanaken but when one-on-one could only fire wide of the post, after Wes Morgan had been convincingly outpaced.
But just moments later Leicester stole the lead, taking advantage of a lack of communication between the hosts' goalkeeper Ludovic Butelle and Vanaken.
Butelle came to clear Hernandez's long throw-in, only for Vanaken to flick the ball out of his 'keeper's reach with a header, unwittingly giving it straight to Marc Albrighton at the far post.
The winger, released by Aston Villa in the summer of 2014, simply needed to tap into an empty net for the Foxes' first ever goal in the competition and their first in Europe since September 2000.
The East Midlands outfit soon settled after their goal and were content to give Brugge the lion's share of possession, in the knowledge that they could sit back and limit them to few chances.
They did just that, denying the home side any time or space in their final third by staying compact and rigid as a defensive unit.
Izquierdo was Brugges' most threatening player, using his pace to get the better of Hernandez down the left-hand side before cutting in and firing high and wide of Kasper Schmeichel's goal.
Stunning Mahrez free-kick puts Leicester in control
But Leicester were the more lively of the two teams going forward, and Brugges captain Timmy Simons went into the book for bringing down Vardy on the break when he could arguably have been sent off for denying the striker, who had a clear run at goal, a goalscoring opportunity.
However, Riyad Mahrez's resulting free-kick ensured the decision needn't matter - sending a powerful swerving left-footed effort beyond the wall to beat the goalkeeper on his side of the wall and double Leicester's advantage.
That filled them full of confidence, with Danny Drinkwater showing the audacity to shoot from a 40-yard free-kick - although his well-struck attempt was a relatively simple save for Butelle.
Leicester were fully on top, goalscorer Mahrez sharing a one-two with Slimani ea on the edge of the area before curling an effort which deflected just wide of the far post after taking a nick off Simons.
They continued to ask questions of Butelle, who was forced to tip over Drinkwater's incredibly well-executed volley from a corner as it almost dipped beneath his crossbar.
Vardy soon went close to adding a third for the visitors before the break, but was forced to shoot from an acute angle which allowed Butelle to beat away his powerful strike and keep the deficit at just two at half-time.
Brugge started the second-half well, Hernandez forced to put Ricardo Van Rijn's teasing cross out for a corner which Stefano Denswil headed wide from Ruud Vormer's delivery, but they could not create any real chances.
Slimani's blatant push through the back of Engels, frustrated after the defender shielded a loose ball for his goalkeeper to collect, forced Brugges to temporarily play with 10 men around the 50-minute mark.
Engels received treatment before being rushed down the tunnel, with the Belgian looking to have dislocated his shoulder when he crashed to the turf, before Preud'homme was forced to replace him with Benoit Poulain.
Leicester were comfortable, with Schmeichel making his first save of the game by collecting Izquierdo harmless's effort.
Mahrez despatches penalty to put result beyond doubt
Immediately afterwards, the visitors could have made it 3-0 when Poulain's underhit backpass almost invited Slimani to round the 'keeper and fire into an empty net.
The onrushing Butelle did enough to prevent the Algerian from winning the loose ball before substitute Poulain recovered from his error to clear.
It was Slimani's strike-partner, Vardy, who eventually helped force the third of the evening when he used his pace to steal in and intercept another poor pass across the back, this time from Simons, and drive through on goal.
Butelle came out to meet him, but the Englishman's fine footwork allowed him to take it beyond the 'keeper - who could only bundle Vardy over to concede a penalty.
Mahrez, having missed three of his last four penalties, retained his spot-kick duties and fired down the middle to give Leicester a commanding lead and all but seal the three points with a third of the game left.
The Blue-Blacks had a good opportunity to reduce the deficit immediately as Izquierdo's touch wrong-footed Morgan inside the box, allowing the forward to cut onto his right foot and fire a shot which bounced back off the far post with Schmeichel well beaten.
The lead allowed Ranieri to hook Vardy and Mahrez well before full-time, adding the pace of Ahmed Musa and Demarai Gray, who flashed a shot just wide in the final stages, to keep Brugges busy.
Brugge looked for a late consolation but Ranieri's back-line stayed strong to seal a deserved clean sheet and the ideal start to life in Group G - which they top after matchday one due to Copenhagen and Porto's 1-1 draw in the other game in Portugal.