There was little evidence of first night nerves as winger Marc Albrighton opened the scoring within the opening minutes before Riyad Mahrez converted two set pieces; a stunning free-kick in the first half and penalty in the second.
Victory, coupled with FC Copenhagen’s draw in Porto, propelled Leicester to the top of Group G.
“I said to them when you listen to the music, it is a big charge, charge your batteries and fight,” said Ranieri. “It was an important win for us, very, very important. We scored very early and that gave us more confidence.”
Leicester stormed into a fifth-minute lead when Albrighton forced the ball home from inside the six-yard box after Luis Hernandez’s long throw was headed beyond the grasp of his own goalkeeper by Hans Vanaken.
The Foxes doubled their advantage shortly before the half-hour mark as Mahrez curled a stunning free-kick over the wall and beyond Brugge stopper Lodovic Butelle.
Ranieri’s side settled matters and wrapped up their maiden Champions League victory as Mahrez dispatched a penalty after Vardy, a menace all evening, had been felled by Butelle.