The Reds were second best for long spells as Leicester kept them on the back foot, but first-half goals from Sadio Mane and Roberto Firmino proved to be enough for them to make it four wins from four at the start of the 2018-19 campaign.
Leicester pulled a goal back through Rachid Ghezzal in the second half following a glaring error from Alisson Becker, who conceded for the first time as a Liverpool player, but it did not prove too costly as Jurgen Klopp's side held off some heavy pressure to maintain their 100% record.
The visitors should have broken the deadlock as early as the fourth minute when Firmino collected a pass inside the box before drawing a low stop from Kasper Schmeichel, although the biggest chance fell to Mohamed Salah from the rebound when he somehow placed his finish wide of the target.
An early goal did arrive shortly afterwards, though, as Andrew Robertson burst down the left flank before pulling the ball back for Mane, who capitalised on a stroke of luck off Harry Maguire before poking his finish past the keeper from close range.
It was a deserved lead for Klopp's side following their quick start to the match, and for much of the opening 20 minutes it looked as though they might add to their advantage, with Joe Gomez sending one header off target from James Milner's corner.
Leicester slowly began to grow into the match, though, and they tested Alisson for the first time midway through the first half when Demarai Gray broke into the box and went for goal, drawing a smart low stop from the Liverpool keeper.
Suddenly it was the home side who were seeing most of the ball with Liverpool struggling to get out, but Leicester were largely limited to long-range efforts from Marc Albrighton, Ben Chilwell and the impressive James Maddison.
Salah did have a chance to double Liverpool's advantage towards the end of the half when he saw a low curling effort tipped behind by Schmeichel, but from the resulting string of corners the Reds did grab a second goal against the run of play.
Firmino escaped the attentions of Maddison to power a downward header into the bottom corner, beating Schmeichel's despairing dive for his first goal of the season.
It gave Liverpool a flattering lead at the interval, but Leicester did not let their heads drop and picked up where they left off at the start of the second half with Ghezzal feeding a low cross/shot narrowly wide of the far post.
Maddison continued to look like Leicester's best player, and the summer signing drew one save from Alisson before dancing into the area and only being denied a goal by a brilliant last-ditch block from Gomez.
Leicester kept up their pressure, though, and Wilfred Ndidi forced another save from Alisson before Wes Morgan squandered their clearest chance of the opening hour when he could not sort out his feet in time to convert a cross from close range.
Liverpool's own sights of goal were few and far between, and when they did arrive the attacking unit looked a far cry from the one which had been tipped to fire the Reds to a title challenge this season, with Salah's misplaced reverse pass for Milner seeing one particularly good platform go begging.
Leicester did finally get their deserved goal shortly after the hour mark, and it was a moment to forget for Alisson, whose bright and unbeaten start to life as Liverpool goalkeeper came crashing down with an unnecessary risk to gift the Foxes one back.
The Brazil number one tried to take the ball past Kelechi Iheanacho on his own byline, but got it caught under his feet, allowing the Leicester striker to rob him of possession and tee up Ghezzal, who kept his composure to become the first player to score past the Reds this season.
At that stage it looked as though Leicester would push on to get at least a draw from the game, with Liverpool struggling to stifle the hosts' momentum or build any of their own during an uncharacteristically sloppy and lacklustre performance.
However, Claude Puel's side could not turn their pressure into goals, and Klopp's surprise decision to withdraw Salah and captain Jordan Henderson with a little under 20 minutes remaining helped the Reds to regain a degree of control over the game.
Indeed, it was Liverpool that created the better half-chances during the closing stages with Mane and Trent Alexander-Arnold failing to hit the target, although the full-time whistle will have still come as a relief to the visitors.
The victory means that Liverpool have now won their opening four games of a top-flight season for the first time since 1990-91, lifting them three points clear of Tottenham Hotspur, Chelsea and Watford, all of whom have also made 100% starts to the campaign.
LEICESTER (4-2-3-1): Schmeichel; Pereira, Morgan, Maguire, Chilwell; Mendy, Ndidi; Ghezzal, Maddison (Amartey 83'), Albrighton (Iheanacho 61'); Gray (Okazaki 76')
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold (Matip 89'), Gomez, Van Dijk, Robertson; Wijnaldum, Henderson (Keita 71'), Milner; Salah (Shaqiri 71'), Firmino, Mane