The Foxes striker outscored Arsenal striker Pierre-Emerick Aubameyang (22), Southampton's Danny Ings (22), and Manchester City forward Raheem Sterling (20).
Manchester City's Brazilian keeper Ederson won the Golden Glove award and Kevin De Bruyne won the Playmaker award.
Jamie Vardy was forced to come off as Kelechi Iheanacho replaced him in a game where Leicester were leading 2-0 at half-time.
Rodgers left defender Chilwell and midfielder Choudhury out of the Foxes' squad for the 2-1 defeat at Burnley.
Leicester are just five points behind league leaders Liverpool, who host Tottenham Hotspur on Sunday, after a historic display that sank the Saints.
Vardy, who scored 24 goals in Leicester's unlikely title triumph in the 2015/16 season, said a united dressing room was a key factor in building a successful team.
Leicester City boss Claude Puel believes Riyad Mahrez is in better shape than before his self-imposed Foxes exile.
Riyad Mahrez's first Premier League goal of the season secured Leicester a 1-1 draw with West Brom on Monday.
The Foxes' appeal to FIFA to secure the registration of Silva was last week rejected by world football's governing body.
The appeal was rejected despite FA support as the paperwork was submitted 14 seconds late on deadline day.
Coutinho marked his first Premier League start of the season with a superb goal as Liverpool returned to winning ways.
Portugal midfielder Adrien Silva has been unable to train and remains in limbo as Leicester City bid to sort out his future.
Leicester City agreed a 24 million euros deal with Sporting Lisbon for the 28-year-old Adrien Silva on August 31.
Supporters from both Leicester and Brighton took to social media after the match to express concern about the abuse.
Arsenal manager Arsene Wenger expressed relief over Olivier Giroud's decision to stay with the Gunners.