First-half goals from Sadio Mane and Roberto Firmino put Liverpool in control at the King Power Stadium before the hosts hit back thanks to Alisson’s gaffe.
His error, which saw him robbed of possession by Kelechi Iheanacho and resulted in Rachid Ghezzal slotting home, was the first goal the Brazilian has conceded since his £67million summer move from Roma.
But Liverpool survived to record their fourth straight win and continue their flying start to the campaign.
Leicester battled well and worried the visitors but failed to cash in once they had Liverpool on the ropes.
Ultimately, the Foxes paid the price for a slow start and Mohamed Salah missed a sitter after just four minutes when the usually lethal forward sidefooted wide from 10 yards after Kasper Schmeichel denied Firmino.
Salah’s slip was a collectors’ item and Mane showed him a clinical edge just six minutes later.
There had already been some worrying gaps in the Leicester defence and Mane capitalised on a lucky ricochet to open the scoring.
Andrew Robertson bundled his way down the right and Harry Maguire deflected his cross to Mane and the forward poked past Schmeichel.
A goal up, Liverpool settled and dominated, toying with their hosts as Firmino and Salah waltzed through the Foxes’ lines and Georginio Wijnaldum’s effort was blocked by Maguire.
Leicester lacked presence and punch without the suspended Jamie Vardy but began to show signs of life after 22 minutes.
A poor touch from Wijnaldum allowed Leicester to gain a footing and Demarai Gray forced Alisson into a low stop.
Leicester were emboldened and with Liverpool no longer in charge James Maddison began to threaten, in front of the watching Gareth Southgate.
The midfielder shot over 10 minutes before the break and found pockets of space to unnerve the visitors.
But, marshalled by Virgil van Dijk the red wall refused to budge and even if they had briefly lost control of midfield there was never a sense Liverpool were in real trouble.
Leicester had gained a foothold, at least, but it was whipped from under them a minute before the break.
Schmeichel, making his 300th appearance for Leicester, turned Salah’s curling effort behind before Firmino pounced.
Leicester defended the initial corner but when James Milner swung the ball in from the other side Firmino brushed off Maddison’s weak challenge to head in.
At 2-0 it was a long way back for the hosts but Maddison almost started the revival six minutes after the break only for Joe Gomez’s excellent covering tackle to deny him.
Wes Morgan then failed to get a proper touch on Ben Chilwell’s cross with Alisson exposed.
Leicester sensed a way back and they grabbed a goal after 63 minutes thanks to Alisson’s calamitous mistake.
The Foxes forced Liverpool into retreat and while Van Dijk’s back-pass pushed Alisson wide the Brazil international was too slow to clear.
His attempt to turn Iheanacho only allowed the striker to steal the ball and cross for Ghezzal to net from six yards.
Liverpool had failed to get going in the second half – missing a four-on-two chance just before Ghezzal’s goal – and paid the price.
But Leicester could not find a second as Jurgen Klopp’s Reds clung on to all three points.
Liverpool captain Jordan Henderson will make his first start of the Premier League season away to Leicester after coming into the side at the expense of Naby Keita.
Henderson is the sole change to the Liverpool side that beat Brighton 1-0 last weekend, as the Reds look to make it four Premier League wins from four before the international break.
Meanwhile Claude Puel has brought in two new names to the Leicester starting XI that was victorious against Southampton, as Marc Albrighton and Rachid Ghezzal get the nod.
Leicester: Schmeichel, Ricardo Pereira, Morgan, Maguire, Chilwell, Mendy, Ndidi, Albrighton, Maddison, Gray, Ghezzal.
Subs: Evans, Iheanacho, Ward, Amartey, Okazaki, Iborra, Fuchs.
Liverpool: Alisson, Alexander-Arnold, Gomez, van Dijk, Robertson, Wijnaldum, Henderson, Milner, Salah, Firmino, Mane.
Subs: Keita, Sturridge, Moreno, Lallana, Mignolet, Shaqiri, Matip.
The Belgium international seemed destined for the exit following the £65million arrival of the Brazilian this summer for what was, at the time, a world record fee for a goalkeeper.
However, Loris Karius – to whom Mignolet lost his place last season – was the one to depart earlier this week on a two-year loan to Besiktas, with the Turkish club undertaking a option to buy for a further £7.25m should he meet certain appearance and European qualification criteria.
It left Mignolet facing another campaign as second choice and prompted him to give an interview in his homeland in which he said he still wanted to play and did not know what the future held for him.
Klopp was not happy the goalkeeper went public but understood his frustrations.
“It is true he will not depart, of course not,” he said ahead of Saturday’s early kick-off at Leicester.
“In general discussing your individual problems in public does not make too much sense, it is better to speak to each other, I’m a big believer in that. But it was still OK.
“We are all human beings and I have no problem with that, and if he was happy to be a number two then I wouldn’t really know him.
“He is a top professional, a top goalkeeper and of course he is not happy to be number two but at the end there are worse things in the world than being number two – pretty good pay by the way at Liverpool.
“In the first moment you understand decisions or not but it is always better to talk to me directly about it than to newspapers.
“It makes not too much sense, if you want to say something to me say it directly – that helps.”
Klopp took a different view, however, with Mohamed Salah‘s ongoing feud with the Egyptian football Association.
The forward has been in dispute with the organisation since before this summer’s World Cup over image rights.
There were further issues at the tournament, as the Egyptian FA decided to set up their training base in Grozny, leading to Salah being pictured with controversial Chechen leader Ramzan Kadyrov.
On Sunday Salah posted a message on Twitter which said: “It’s normal that a football federation seeks to solve the problems of its players so they can feel comfortable but really, what I see is exactly the opposite.
“It’s not normal that my messages and my lawyer’s letters are ignored. I do not know why this is all (happening)?”
Ramy Abbas, Salah’s lawyer and agent, sought to clarify the comments, saying they had asked for guarantees regarding Salah’s well-being while with the national team and assurances image-rights violations would not happen again.
Salah subsequently posted two videos to Facebook insisting he was asking for better security for the whole team, detailing how he did not want to be disturbed in his room by visitors wanting to chat in the middle of the night as had happened previously.
Despite the usually reserved Salah being so outspoken Klopp said he had no concerns over the player becoming distracted.
“About the thing with the Egyptian FA I can’t say too much, it is really something between the player and the FA,” he said.
“I spoke to Mo about that but it is not for us to intervene in that moment, to say something about that. They will solve that, I am sure.
“It is not about me so it is really between Mo and the FA, that is all I can say about that.
“As long as they talk about us pretty much everything is allowed – well maybe not everything, but a lot.”