Marc Albrighton netted the Foxes’ first-ever Champions League goal, and first in Europe since 2000, before Riyad Mahrez crashed in a brilliant free-kick.
Mahrez made it 3-0 with a second-half penalty with Leicester, who dominated at the Jan Breydel Stadium, top of Group G after Porto and Copenhagen drew 1-1.
Burnley will give the Foxes a sterner test than abject Brugge when they return to the Premier League on Saturday and Leicester must learn to cope with the demands of the league and European football.
But it was the perfect performance from the Foxes, 50-1 to win the competition after last season’s shock Premier League victory, although things could have been so different if the hosts had taken a glorious opportunity after two minutes.
Abdoulay Diaby skipped through Danny Drinkwater’s lunge and slipped in Jose Izquierdo but the forward’s finish was woeful and he was made to pay three minutes later when Albrighton wrote his name into the Foxes’ history books.
It was scrappy stuff and a gift as Brugge got into an almighty mess but sent the travelling 1,400 Leicester fans into raptures.
Luis Hernandez launched a long throw into the box from the right and Ludovic Butelle came to punch but the ball brushed off Hans Vanaken’s head and fell for the onrushing Albrighton to fire in from six yards.
Leicester instantly relaxed with Brugge unnerved and looking lost as they struggled to find any fluency. They played into the Foxes’ hands as Mahrez began to exploit the extra space and Jamie Vardy remained an irritant.
Izquierdo blazed well over to underline how weak the hosts were going forward and it then got even better for the Foxes after 29 minutes.
Again, Brugge made a hash of it at the back and captain Timmy Simons was booked for chopping down Vardy on the edge of the box after he lost the ball.
It gave Mahrez the chance and it was one he did not pass up as the winger whipped a delicious 20-yard effort across Butelle into the top corner.
Stunned, Brugge had no response and Leicester went in search of a third as Mahrez curled wide and Drinkwater twice tested Butelle, the second a dipping 30-yard volley.
The lively Vardy almost made it three before the break when Butelle spilled his angled drive as the Belgians continued to be accommodating and generous hosts.
There was little to suggest they would change after the break as record buy Islam Slimani, making his debut, began to threaten, although he was booked for a needless push on Bjorn Engels which saw the defender substituted with a serious looking shoulder injury. And more defensive calamity from Brugge gifted Leicester a third when Mahrez completed his double with a penalty after 61 minutes.
Vardy hassled Stefano Denswil into losing the ball and the England striker raced through only to be taken out by Butelle and Mahrez gleefully converted from the spot — despite missing three of his previous four penalties.
Diaby clipped the post as powderpuff Brugge tried to find a way back but Leicester even had the luxury of giving Vardy, Mahrez and Slimani a rest as Ahmed Musa, Leonardo Ulloa and Demarai Gray replaced them.
And Gray almost put the gloss on a brilliant team performance when he fired over after a darting run with six minutes left.
Butelle, De Bock, Denswil, Engels (Poulain 53), Van Rhijn, Vanaken, Pina, Simons, Vormer, Diaby (Vossen 63), Izquierdo (Felipe Gedoz 77).
Bruzzese, Claudemir, Cools, Bolingoli Mbombo.
Schmeichel, Hernandez, Morgan, Huth, Fuchs, Albrighton, Drinkwater, Amartey, Mahrez (Gray 80), Slimani (Ulloa 62), Vardy (Musa 70).
Zieler, Chilwell, King, Wasilewski.
Tasos Sidiropoulos (Greece).