Eoghan O'Connell cancelled out a Riyad Mahrez opener in normal time to force the shootout, and it was the English champions who came out on top from the spot, beating the Scottish champions 6-5 to win the Battle of Britain.
The first ever meeting between the two sides got off to a fairly quick start, and Leicester had a chance inside three minutes when Marc Albrighton shrugged Scott Brown off the ball before playing a low pass into the box that Danny Drinkwater could only slice into the body of Emilio Izaguirre.
Both sides were looking to play attacking football, but the best chances in the first half fell the way of the visitors and they squandered two more in the opening 10 minutes when first Wes Morgan saw a header from a corner hit a defender before Mahrez blazed the rebound over the crossbar.
The Foxes' best chance of the opening 45 minutes arrived soon after when Leonardo Ulloa, who is rumoured to be considering leaving the club this summer, was played clean through on goal only to scuff his finish well wide under pressure from Saidy Janko.
Ron-Robert Zieler, making his maiden start for Leicester, was the first goalkeeper called into action when Leigh Griffiths caught Ben Chilwell in possession before racing through, but his curling effort towards the bottom corner was comfortable for the summer signing.
Zieler needed to be a little more alert moments later, though, as Moussa Dembele forced a smart reaction save from the keeper having done well to get a shot away while falling over.
Reigning PFA Player of the Year Mahrez, who has also been linked with a move away from the King Power Stadium this summer, began to grow into the game as the half wore on and he almost provided the opening goal midway through when he collected Drinkwater's diagonal pass before cutting inside and curling his effort narrowly wide.
Mahrez turned provider shortly after the half-hour mark when his cross found Chilwell's marauding run forward, only for the full-back to nod his effort straight at Craig Gordon.
Despite Leicester creating the best chances it was Zieler who was the busier of the two keepers in the opening 45 minutes, and he was called into action again towards the end of the half when he tipped a powerful Griffiths free kick past the post.
Neither side were able to break the deadlock in the first half, but that changed within one minute of the restart when Mahrez opened the scoring in trademark fashion, collecting the ball on the right flank before cutting inside and curling his finish into the far corner.
The hosts were back level shortly before the hour mark, though, and it was another tidy finish as O'Connell steered a first-time shot into the bottom corner after a loose ball had broken to him just outside the area.
The two goalscorers came face to face with each other in the 67th minute when Mahrez received the ball again on the right flank, skipping past O'Connell with ease only to play his cross behind Ahmed Musa with the goal gaping.
Chances dried up at both ends of the field towards the closing stages of the match, but there was one last opening for Leicester in the final minute of the 90 when Shinji Okazaki glanced a header just over from Danny Simpson's cross.
International Champions Cup rules mean that Leicester get two points for their win via a shootout, while Celtic are awarded one point.