Goals from Sadio Mane and Roberto Firmino in the first half gave table-toppers Liverpool a seemingly unassailable lead.
Leicester deservedly reduced the arrears through Rachid Ghezzal, who punished an embarrassing blunder from Alisson.
It was the first goal Jurgen Klopp's side had conceded in 418 minutes of Premier League football going back to May 6 and the first Alisson had let in club football since last season's Champions League semi-final when he was playing for Roma, against Liverpool.
But Leicester couldn't find the equaliser as Liverpool's defence remained firm in front of Alisson to secure their fourth successive win heading into the international break.
Alisson's counterpart Kasper Schmeichel, making his 300th appearance for Leicester after signing a new contract in midweek, was into the action within the first three minutes.
Mohamed Salah put Firmino through but he could only fire against Schmeichel's legs, and from the rebound, Salah side-footed wide.
The Reds took a 10th-minute lead when Senegal winger Mane made the most of his ricochet off Harry Maguire from Andrew Robertson's cross to bury left-footed to Schmeichel's right for his third goal of the season.
Liverpool remained on top and Joe Gomez sent a header looping well over the bar from Trent Alexander-Arnold's corner.
Leicester's first chance came in the 22nd minute when Demarai Gray got away from a defender to latch on to Ghezzal's pass and squeezed in a shot that Alisson smothered.
The home side continued to find it hard to open Liverpool up, and were being forced to try their luck from distance as James Maddison fired over from long range.
But they had eased themselves into the game and were finally starting to give Klopp's side something to think about.
- Reds held firm -
Just as Leicester might have thought they had turned the tide, Liverpool broke away quickly and doubled their lead.
Salah forced Schmeichel to push his shot around the post, and from their second successive corner, Firmino met James Milner's flag-kick with a firm header into the far corner of the net from 10 yards.
Leicester pressed to reduce the arrears following the restart and Ghezzal surprised Alisson with a low cross that bounced just wide of the far post.
Maddison was the nearly man again in Leicester's next attack, when only the outstretched leg of the lunging Gomez blocked a goal-bound effort after he wriggled past Alexander-Arnold.
Leicester were having their best spell of the game as the hour mark approached.
Wes Morgan failed to sort his feet out from point-blank range after Marc Albrighton and Gray also missed contact from Ben Chilwell’s low centre.
Leicester's persistence was rewarded in the 63rd minute.
And after so much criticism of Liverpool's goalkeeping department in recent years, it was another howler from their last line of defence.
Alisson dallied on a back pass from Virgil Van Dijk and allowed himself to be dispossessed by substitute Kelechi Iheanacho on the byline and he crossed for Ghezzal to steer home
Klopp made a double substitution on 69 minutes in a bid to wrest back control as Naby Keita and Xherdan Shaqiri came on for Henderson and Salah.
The changes made little effect however, although Leicester's charge faded as Liverpool held firm in the closing stages.