- Philip Billing (40')
Leicester created little and were indebted to goalkeeper Daniel Iversen for keeping them in the game.
They were booed off at the end of a dismal display which left them second-from-bottom with 25 points.
Bournemouth moved up to 15th place with 30 points.
Maddison earned rave reviews for his performance for England against Ukraine last month but he suffered a horror moment that condemned his side to another damaging defeat on Saturday.
He attempted to play a pass back to his goalkeeper under no pressure but got it all wrong and massively under-hit it, playing in Billing to slot a shot past Iversen.
Leicester, with Adam Sadler again in charge after the sacking last week of Brendan Rodgers, had looked woefully short of confidence even before going behind.
They rarely looked like salvaging something from a game they badly-needed to win to address their slide with striker Jamie Vardy starved of service.
Bournemouth were impressive and would have won by a wider margin had Iversen not made several fine saves, notably to deny Billing and Dominic Solanke.
Maddison did come close to atoning for his error when his fierce drive was kept out by Bournemouth keeper Neto but it would have been harsh on the visitors had they not taken three points.
Leicester, Premier League champions in 2016, are drifting towards relegation and defender Wout Faes said the club needed to do something soon to stop the rot.
"The club needs to decide about a manager. We don't know anything. I guess they are working on it," he told the BBC. "It is not going to be easy to stay up, but we need to stick together."
- David Coote
|Brighton & Hove Albion||6||5||0||1||+10||15|
|West Ham United||6||3||1||2||+1||10|