Two of the three points were scored by Curtis Jones, brushing aside efforts by Leicester, maintaining their recent winning streak, and coming closer to their goal spot at the Champions League.
The Reds scored two of their three points early in the game, both courtesy of Jones with the help of Mohamed Salah. Jones has now scored three goals in his past four games for the team.
It would have been 3-0 before halftime but Daniel Iversen of Leicester denied Cody Gakpo the chance to score from close range.
Liverpool is now just one point behind New Castle and Manchester United.
As for Leicester, this recent loss puts them in danger of finishing in the 19th spot with only two games remaining.
The Foxes have collected only one win in their last 14 games.
Leicester’s fans left the King Power Stadium with 20 minutes left of the game. They will next face West Ham but their fate is sealed.
The team’s frailties are often blamed on the changes made by head Dean Smith.