First-half goals from Sadio Mane and Roberto Firmino proved enough for the visitors to notch a fourth successive victory, although it would have been easier had Alisson not gifted a first Leicester goal to Rachid Ghezzal.
The Brazil international, unbeaten in his previous three outings, was punished in the 63rd minute for a sloppy attempt at playing out from the back that threatened to derail what was otherwise a comfortable trip to the King Power Stadium.
The error set up a potentially nervy final half-hour, but the Reds ably saw out the contest to seal maximum points from their opening four Premier League outings for the first time in their history.
Liverpool netted three on their last visit to Leicester and they almost matched that tally in an efficient first 45 minutes.
The in-form Mane made up for Mohamed Salah's uncharacteristic early miss by stabbing home a close-range opener in the 10th minute, before Firmino was afforded far too much space to head home James Milner's corner on the stroke of half-time.
Alisson made a smart stop from Demarai Gray between the goals but the goalkeeper was at fault for offering the Foxes a way back into the contest.
The former Roma man compounded Virgil van Dijk's errant back-pass with a casual attempt at turning away from substitute Kelechi Iheanacho, who robbed him of the ball and squared for Ghezzal to open his Premier League account.
But with Jamie Vardy serving the final match of his three-game suspension, the Foxes lacked the cutting edge to further trouble Jurgen Klopp's men, who momentarily stretched their lead at the summit to three points.
60 - Under Jurgen Klopp, Roberto Firmino has been directly involved in 60 Premier League goals (37 goals, 23 assists), 15 more than any other Liverpool player. Favourite. #LEILIV pic.twitter.com/TRQTqoP5O8 — OptaJoe (@OptaJoe) September 1, 2018
What it means: Reds not without fault
Though they will be happy to have banked another three points, conceding for the first time this term in such an awkward manner suggests the league leaders still have plenty of room for improvement defensively.
Pat on the back: Raiding Robertson
Reliable at both ends, Andrew Robertson continually looks one of Klopp's canniest signings since arriving at Anfield. The left-back's value was again obvious with the marauding run he made to single-handedly tee up Mane's opener.
Boot up the backside: Alisson still adjusting
Klopp praised Alisson for having the "confidence" to explore his full range of skills at Anfield last weekend, but the Reds boss might not be so forgiving on this occasion. The 25-year-old only had himself to blame for giving up his clean sheet record, over-complicating what should have been a simple move out from the back.
Key Opta stats:
80 - James Milner has now registered 80 Premier League assists, the same number as David Beckham. Only six players have more in the competition. Interesting. #LEILIV— OptaJoe (@OptaJoe) September 1, 2018
- Leicester have lost their last 11 Premier League matches against sides starting the day top of the table, scoring just five goals while conceding 27 in those matches.
- No player has assisted Liverpool’s Roberto Firmino more times in the Premier League than James Milner (8).
- James Milner made his 100th Premier League appearance for Liverpool today (also 100+ games for Aston Villa and Man City). He is the fourth player to reach 100+ apps for three different Premier League teams alongside Gareth Barry, Rory Delap and Gary Speed.
- Liverpool forward Sadio Mane has had a hand in four goals in his last four Premier League games against Leicester (two goals, two assists).
- Since the start of last season, no player has more league assists in the top four tiers than Leicester’s James Maddison (16), level with Kevin De Bruyne and Barry Douglas.
- Leicester City are the first Premier League team to have three Algerian players score for them in the competition following Rachid Ghezzal’s strike (also Riyad Mahrez and Islam Slimani).
Liverpool are in for a sterner test after the international break as they head to the similarly impressive Tottenham, while Leicester will regroup before a difficult trip to Bournemouth.