The champions paid for a lacklustre first half, where they created clear openings for Jamie Vardy and Robert Huth, but surrendered the ball all too easily.
Eddie Howe's side saw 70% of the ball before the break and Marc Pugh scored for the hosts on his first league start of the season with a controlled drive from 18 yards out.
Leicester improved but ran into a stubborn home defence and goalkeeper Artur Boruc produced a key save to deny Leonardo Ulloa from six yards in the final minute.
Relive Bournemouth's hard-earned win
It means Claudio Ranieri's side set an unwanted record as their haul of one point away from home is the lowest total by a defending top-flight champion from the first eight away games of a season.
They remain 14th, four points above the bottom three, while the Cherries move to eighth.
Boruc's late save followed a key block from Steve Cook to thwart substitute Shinji Okazaki. The two interventions epitomised Bournemouth's resilience and Howe described it as a "heroic" defensive display.
His side had conceded nine goals in three games before kick-off, prompting him to call for more solid showings and that is what he got.
Good home possession early on killed any momentum Leicester hoped to carry from Saturday's thrilling victory over Manchester City.
And Bournemouth's reward for a fifth home win of 2016-17 is to be five points better off than they were at the same stage last season.
Pugh added to the positives with an excellent all-round display, showing good technique in keeping a bouncing ball on target for the winner after Benik Afobe's shot was saved.
Howe - who refused to set a target of European qualification after the win - described the match winner as "the model professional" for his patience in waiting for his chance start a league fixture.
The statistics get uglier for Leicester, who have no back-to-back wins in the league since April.
The Foxes have conceded 19 goals on the road, one more than in all 18 away games last season and have managed 21 goals in 16 games - 13 fewer than at the same stage last term.
And against Bournemouth they looked one-dimensional going forward. They mustered 12 shots but many of them arrived in a late flurry. Vardy - a hat-trick hero three days earlier - had 26 touches, the same number as Islam Slimani, who was taken off at the break and just six more than Okazaki, who replaced the Algerian.
Huth's early volley - deflected wide moments before Pugh's winner - could have significantly changed proceedings but with just 37% possession on the night and only 68% of their passes finding a team-mate, Leicester were not good enough.
Their display on the south coast was confused. They were slow from the off and limited in their reaction until it was too late.
Ranieri - who has now managed 200 games in the Premier League - will have to find answers.
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Bournemouth manager Eddie Howe: "It didn't feel anything like routine. It was dramatic playing the champions, we know their qualities and the lads did particularly well. It was a heroic defensive display. I thought we were magnificent in that respect."
Leicester manager Claudio Ranieri: "The result is too severe against us because we created more chances than Bournemouth. I wanted a little more in the first half. A little more and we can score goals, recover more second balls. The second half was much better. If we continue to fight at this level, sooner or later we will get a good result."
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Bournemouth host their south-coast rivals Southampton at 13:30 GMT on Sunday, while Leicester will look to end their dismal away run by taking points at Stoke City on Saturday (15:00).
Match ends, Bournemouth 1, Leicester City 0.
Second Half ends, Bournemouth 1, Leicester City 0.
Jack Wilshere (Bournemouth) wins a free kick in the attacking half.
Foul by Luis Hernández (Leicester City).
Substitution, Bournemouth. Tyrone Mings replaces Callum Wilson because of an injury.
Delay over. They are ready to continue.
Delay in match Callum Wilson (Bournemouth) because of an injury.
Attempt saved. Leonardo Ulloa (Leicester City) right footed shot from very close range is saved in the centre of the goal. Assisted by Jamie Vardy.
Foul by Charlie Daniels (Bournemouth).
Riyad Mahrez (Leicester City) wins a free kick on the right wing.
Harry Arter (Bournemouth) wins a free kick in the defensive half.
Foul by Leonardo Ulloa (Leicester City).
Offside, Bournemouth. Jack Wilshere tries a through ball, but Callum Wilson is caught offside.
Luis Hernández (Leicester City) is shown the yellow card for a bad foul.
Callum Wilson (Bournemouth) wins a free kick on the left wing.
Foul by Luis Hernández (Leicester City).
Corner,  Leicester City. Conceded by Steve Cook.
Attempt blocked. Shinji Okazaki (Leicester City) right footed shot from the centre of the box is blocked. Assisted by Riyad Mahrez.
Attempt missed. Marc Pugh (Bournemouth) right footed shot from outside the box is high and wide to the right. Assisted by Adam Smith.
Marc Pugh (Bournemouth) wins a free kick on the left wing.
Foul by Luis Hernández (Leicester City).
Wes Morgan (Leicester City) is shown the yellow card for a bad foul.
Jack Wilshere (Bournemouth) wins a free kick in the defensive half.
Foul by Wes Morgan (Leicester City).
Corner,  Leicester City. Conceded by Steve Cook.
Corner,  Leicester City. Conceded by Simon Francis.
Attempt blocked. Riyad Mahrez (Leicester City) right footed shot from the right side of the box is blocked. Assisted by Leonardo Ulloa.
Substitution, Leicester City. Leonardo Ulloa replaces Robert Huth.
Foul by Steve Cook (Bournemouth).
Jamie Vardy (Leicester City) wins a free kick in the attacking half.
Offside, Bournemouth. Steve Cook tries a through ball, but Callum Wilson is caught offside.
Substitution, Bournemouth. Dan Gosling replaces Joshua King.
Jack Wilshere (Bournemouth) wins a free kick in the defensive half.
Foul by Daniel Amartey (Leicester City).
Hand ball by Riyad Mahrez (Leicester City).
Attempt missed. Shinji Okazaki (Leicester City) right footed shot from outside the box misses to the right.
Attempt missed. Robert Huth (Leicester City) header from the centre of the box is close, but misses to the left. Assisted by Riyad Mahrez with a cross following a corner.
Corner,  Leicester City. Conceded by Jack Wilshere.
Substitution, Leicester City. Ahmed Musa replaces Marc Albrighton.
Corner,  Leicester City. Conceded by Nathan Aké.
Bournemouth moved to the highest league position in their history as Leicester's miserable run away from home continued with defeat at Vitality Stadium.