Sadio Mane continued his impressive start to the season as he netted in the tenth minute, finishing powerfully from inside the area.
However, Leicester were given hope when Alisson's error saw him being dispossessed by Kelechi Iheanacho, who crossed for Rachid Ghezzal to score.
The Foxes pressed a lethargic looking Liverpool side, but Jurgen Klopp's side held on to secure the three points and remain at the top of the Premier League table.
Liverpool: Alisson, Alexander-Arnold, Gomez, Van Dijk, Robertson, Milner, Henderson, Wijnaldum, Mane, Salah, Firmino.
Subs: Mignolet, Keita, Sturridge, Moreno, Lallana, Shaqiri, Matip.
This video is no longer available.