A Jonny Evans own-goal and Diogo Jota’s strike put Liverpool in cruise control before the break, the Portuguese becoming the first Liverpool player to score in his first four home league appearances.
Roberto Firmino had been denied by the woodwork and the most marginal of goal-line clearances before adding his name to the scoresheet with a superb header to seal a 3-0 win.
The result moves defending champions Liverpool level on 20 points with leaders Tottenham Hotspur while Leicester are fourth, level on 18 points with third-placed Chelsea.
Liverpool grabbed the lead in the 21st minute when Evans, under pressure from Sadio Mane, headed a James Milner corner into his own net.
Leicester responded with a smart break with Jamie Vardy finding Harvey Barnes in a promising position but the left-winger's effort was well wide of the target.
Liverpool's second was a masterfully worked goal with Andy Robertson whipping in a delicious cross from the left which Jota met at the near post with an expertly angled glancing header.
Leicester keeper Kasper Schmeichel pulled off a series of saves to deny the home side after the break while Firmino twice hit the post and had an effort cleared off the line.
The Brazilian, who had scored just twice in his last 23 Premier League games, got his reward four minutes from the end with a fine header from another Milner corner.
Additional reporting by Reuters.