Ayoze Perez got the ball rolling with an early goal before Harvey Barnes doubled that lead.
The Foxes found themselves under sustained pressure during the game but Victor Osimhen's showed his class with two second half goals.
Patson Daka also saw his wait for a Leicester goal go on as he was denied by VAR having put the ball in the back of the net.
The £23million signing partnered Kelechi Iheanacho up front, with Jamie Vardy named among the substitutes.
Midfielder Boubakary Soumare was handed his full debut after a £17million summer move from Lille.
It was Perez who fired Leicester ahead after just nine minutes at the King Power Stadium, which was in brilliant voice for the occasion.
Barnes swapped passes with Wilfred Ndidi to launch a deep cross for Perez to volley in at the far post.
The Foxes have a knack of winning games when the forward gets on the scoresheet, and have a 100 per cent record when he does.
In the eight games Perez had scored in before playing Napoli, they had won all of them and that went on to be nine.
Leicester were perhaps fortunate to go into the break 1-0 up with Napoli having a barrage of opportunities.
Osimhen, Hirving Lozano, Piotr Zielinski and Kevin Malcuit all missed fine first-half chances, with Kasper Schmeichel making a number of fine saves.
Against the run of play Daka thought he had made it 2-0 when he collected Youri Tielemans' pass and drilled in his first goal for the club from 16 yards out.
But it was ruled out by VAR for offside as replays showed he was just ahead of the defender.
Five minutes later, though, Leicester did double their lead when Kelechi Iheanacho found Barnes and the winger shot low into the corner.
Napoli pulled a goal back, though, when Victor Osimhen finished a quick move by lifting over Schmeichel to make it a nervy end to the match.
Osimhen then made it 2-2 with three minutes left when he headed in from eight yards.