Bournemouth looked set for their second league win in a row when striker Callum Wilson showed great athleticism and technique to register his side's first-ever home goal in the top flight.
But City took advantage of the home team's injury misfortune and grabbed a late equaliser through striker Jamie Vardy.
The Foxes drop to third in the league due to Crystal Palace's shock win at Chelsea, while Bournemouth's solid start to the campaign sees them occupy 11th spot.
Leicester manager Claudio Ranieri recalled in-form winger Riyad Mahrez, the league's top goalscorer going into the latest round of fixtures, after resting him for the midweek League Cup victory over Bury.
The visitors quickly made their mark on the match, with Ivory Coast winger Max Gradel earning a booking within the first minute for a bad foul on the tricky winger.
Mahrez thought that he had his revenge a few minutes later, but the linesman ruled that he was marginally offside as he finished past Bournemouth goalkeeper Artur Boruc.
But it was the home team who broke the deadlock through their own in-form forward Wilson.
The 23-year-old former Coventry striker, who scored a hat-trick in last week's win at West Ham, fired the ball into the top left-hand corner from inside the penalty area after 24 minutes for his fourth goal of the campaign.
The strike inspired confidence in the home side as they took full control of the match, with Foxes' goalkeeper Kasper Schemichel denying Gradel from long range.
Mahrez's miserable afternoon ended at half time as Ranieri hauled him off, to be replaced by Shinji Okazaki.
City began the second half in much the same fashion as the first with defender Robert Huth receiving an immediate yellow card, but the home fans were baying for a red as the German defender smashed the ball into Wilson's face as the striker lay on the turf.
The Cherries suffered a blow 10 minutes into the second half when full-back Tyrone Mings, who had only come on as a substitute at half time, was carried off following a nasty collision with Leicester midfielder Danny Drinkwater.
The injury left Bournemouth manager Eddie Howe with no more substitutes and disrupted the home team's dominance, with the visitors growing into the game and testing Boruc with a series of crosses.
The pressure finally paid off four minutes from time when good work from City striker Vardy drew the season's surprise package level and denied Bournemouth their first top-flight home win.
The former non-league attacker earned a spot kick after a driving run at the home defence, and picked himself up to convert the penalty via Boruc's hand. Â
The visitors pushed hard for the win during eight minutes of injury time but Boruc was able to keep them at bay to earn a precious point.