After an even start on the south coast, Ryan Fraser rounded off a ruthless counter-attack by cutting inside and curling into the bottom corner with 19 minutes gone.
Two opportunities for James Maddison followed. First, his free-kick was blocked by the Cherries wall before Asmir Begović made a double save, first denying Jamie Vardy prior to flicking Maddison’s shot onto the crossbar.
Just as the Foxes appeared to be gaining a foothold in the game, the hosts made it 2-0. From another swift move, Callum Wilson found Fraser, who got enough on the ball to slip it past Kasper Schmeichel.
Then, shortly before the break, the Cherries were awarded a penalty after the ball flicked up and hit Ricardo Pereira’s hand. Joshua King converted to put Eddie Howe’s men into a commanding 3-0 lead.
Opportunities followed for Leicester after the interval. Maddison’s low strike was held by Begović, Wilfred Ndidi headed over and Harry Maguire was also denied in a short space of time.
City couldn’t find a breakthrough and they were further frustrated when skipper Wes Morgan was dismissed on 69 minutes after receiving two yellow cards for fouls on King and Adam Smith.
Schmeichel did brilliantly to deny King from a one-on-one situation with 12 minutes to play, but he could do nothing about Bournemouth’s next effort, which was converted by substitute Smith.
After the returning Vardy made way – the striker appearing to pick up a knock – Maddison pulled one back from the spot on 88 minutes following Diego Rico’s foul on Ricardo.
A minute later, substitute Marc Albrighton scored a second by heading in Kelechi Iheanacho’s pin-point cross, and while Ben Chilwell went close in injury time, the Foxes couldn’t complete a remarkable comeback.
Major moment
With Bournemouth leading 1-0 thanks to Ryan Fraser’s opener, the Foxes went in search of an equaliser and only a double stop from Asmir Begović kept out Jamie Vardy and James Maddison, whose effort hit the underside of the bar.
The timing of the Bosnian’s double-save was crucial for the Cherries on Saturday.
Who impressed?
James Maddison, a summer arrival from Norwich City, deservedly claimed his second Premier League goal in Leicester City colours having previously been denied by Asmir Begović in the first half.
He continued to show his creativity on the south coast and will no doubt be a key man for the Foxes in their upcoming fixtures.
Where do we stand?
After five 2018/19 Premier League fixtures, Claude Puel’s men sit ninth in the Premier League table having accumulated six points.
Coming up…
The Foxes return to King Power Stadium on Saturday 22 September for a Premier League clash with Huddersfield Town (3pm BST kick-off).