The hosts were dominant throughout and were given the perfect start as skipper Wes Morgan flicked in Ben Chilwell's effort. Various chances were missed by the East-Midlanders before Jamie Vardy thundered home a header in 82nd minute to make sure of the three points and lift them to eighth in the Premier League table.
Story of the Match
Captain Morgan bags again
It was a confident start from Rodgers' troops and they claimed an early lead as Morgan opened the scoring. James Maddison's corner fell to Chilwell on the edge of the area, with the England defender composing himself for a shot. The ball then fell to the 35-year-old and a clever back-heel saw it trundle into the back of Asmir Begovic's net via the post for his second goal in as many games following last weekend's winner over Burnley.
Despite Leicester's excellent start to the game, Eddie Howe's men could have been level as Callum Wilson stabbed the ball towards goal only for Kasper Schmeichel to pull off an excellent reaction save to deny the striker.
Leicester spurn chances but secure three points
The Foxes' lead could have been extended even further before the break as Ricardo Pereira picked out the unmarked Vardy but he somehow skewed his low effort wide. Another clever move then saw Maddison wriggle free in the Bournemouth penalty area only to see his shot find the gloves of Begovic.
Vardy then also fired a low effort into the midriff of the Cherries' stopper as Leicester probed for a second-goal.
Despite the missed chances for the side, there was never a feeling of anxiety or worry that supporters may have experienced under Rodgers' predecessor Claude Puel. The atmosphere improved even further in the 61st minute as the entire stadium rose to their feet for a stunning tribute to Vichai Srivaddhanaprabha.
The points were eventually secured in style as Youri Tielemans, who was inspired all afternoon, produced a stunning cross. Vardy had managed to find space between Chris Mepham and Nathan Ake to meet the ball and power it onto the crossbar and into the back of the net.
Rodgers has his impact
It is fair to say that Brendan Rodgers has had a huge impact since arriving at the King Power Stadium. The Foxes seem reinvigorated under the Northern Irishman and are playing a brand of football that had long since been forgotten at the King Power Stadium.
The Foxes have now put together a useful run of three consecutive Premier League victories, the first time that they have managed that since December 2017. They have also managed to end their hoodoo against AFC Bournemouth. If Rodgers can continue that positive impact in the East-Midlands, he could potentially take the club extremely far.
'Sign him up'
They were the chants as Youri Tielemans' delicious cross picked out the head of Jamie Vardy for the second goal of the day - and it really is difficult to argue against that. The young Belgian has been a hit since arriving from AS Monaco on loan having notched a goal and four assists in only seven appearances.
He really has given the Foxes midfield more composure, whilst he also provides a crucial attacking outlet. It would surely be a huge mistake should the club not attempt to secure his signature on a permanent basis.
Cherries away day woes
The statistics are really not good reading for Bournemouth fans. In 16 matches away from the Vitality Stadium this season, they have lost 12. In eight of those games, they have failed to find the back of the net. That really is not good enough for a side who want to be pushing for the top-half of the Premier League.
At the King Power, Howe's men were second-best once again. The 2-0 deficit flattered the visitors somewhat and they failed to proved an attacking threat of their own on yet another difficult day away from home.