The England playmaker's dreadful backpass opened the door for Philip Billing to score the only goal of the game in the first half, as the beleaguered Foxes began the post-Brendan Rodgers era with a deserved defeat.
Amid talk of Jesse Marsch potentially taking the reins at the King Power, Leicester's current incumbents had their hearts in their mouths with just five minutes gone, as a Billing free kick struck the woodwork before bouncing harmlessly away.
Down the other end of the field, Timothy Castagne sent an 18-year effort a whisker wide of the post just five minutes later, as both sides showed plenty of attacking endeavour in the opening exchanges.
Pretty soon, Gary O'Neil's men were the ones turning the screw as Leicester faced a barrage of attacks, and the Foxes were fortunate not to have been a goal down when Dominic Solanke fired wide with plenty of time and space on his side in the box with 27 minutes gone.
So often the creator of Leicester's goals, Maddison was the architect of Bournemouth's deserved opener in the 40th minute, as a horribly misplaced backpass allowed Billing to steal in and slot home into the bottom corner with Daniel Iversen in no man's land.
There was little that the Foxes number one could do, but Iversen single-handedly prevented Bournemouth from doubling their lead after the restart, keeping out all of Solanke, Jack Stephens and Chris Mepham within the opening five minutes of the second period.
Boos soon start to ring out from the home faithful as Bournemouth's total domination continued, but the introductions of Patson Daka and Kelechi Iheanacho breathed new life into the hosts, who quickly began to take the game by the scruff of the neck in search of an equaliser.
An injury to Harvey Barnes would immediately hinder Leicester's chances of clawing themselves back into the match - Tete came on to replace the stricken Englishman - and the hosts were quelled by the Cherries henceforth.
Leicester's relegation fears continue to grow as they remain 19th in the Premier League table ahead of a trip to champions Manchester City next Saturday, while Bournemouth have risen to 15th as they prepare to meet Tottenham Hotspur next week.