Darwin Nunez, Bobby Clark, and Diogo Jota all scored within eight minutes of each other in the first half, and Ben Doak added a fourth after the break.
Midfielders Alexis MacAllister and Dominik Szobozlai both played as the Reds seek to rebuild their midfield.
Patson Daka had the finest chance for Leicester late on, but he was denied by a last-ditch Jarell Quansah block.
Liverpool news, analysis, and opinions from fans
Nunez started half of Liverpool’s Premier League games last season, and Jurgen Klopp feels his “readiness to defend” will be his ticket into the team.
The striker was sent off in his second game for the Reds after coming in June, and he struggled for starts following the January transfer of Cody Gakpo from PSV.
“I don’t think I have to tell our fans, it’s pretty much traditionally – or historically – for us that usually players for us, especially offensive players, [need time],” Liverpool manager Jurgen Klopp explained.
“I think Darwin showed some really good signs last season.” Injuries and a red card didn’t help matters at first, but everything worked out in the end. They are all a threat, and they are all terrific footballers – the ticket into the team will be defense readiness, since you never hear about a team being truly successful with sloppy defending; it simply does not happen.
“It’s the same for Darwin as it is for all the other strikers because I know the quality they have and they need to do both, just like our other players have to do – defend and be influential in all offensive situations.”
Nunez scored nine league goals for the Reds after coming from Benfica for an initial fee of £64 million, and Klopp claims the 24-year-old was a “handful” against the Foxes.
