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.