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Liverpool striker Christian Benteke's first goal since the end of October inflicted Leicester's first defeat in three months to open up a crack in their armour.
Claudio Ranieri's side, who failed to score for the first time this season, have profited from a killer counter-attacking game but were nullified until the final quarter, by which time the hosts had already edged ahead.
The 63rd-minute goal came from two players who were far from their best - Benteke started on the bench and benefited from a first-half injury to Divock Origi while Roberto Firmino looked lost for long periods before providing the chance for Benteke.
That will not have mattered to Jurgen Klopp after four matches without victory.
Whether defeat, their first away from home since March, is the bursting of the Foxes' bubble remains to be seen but with Manchester City up next at home this, as expected, will be the most testing period of their campaign.
In an attempt to give his side a better chance of making - and taking - chances, Klopp left out defensive midfielder Lucas Leiva and paired Jordan Henderson and Emre Can in the centre with the attacking trio of Philippe Coutinho, Firmino and Adam Lallana supporting Origi.
Liverpool's lone striker justified his inclusion for 38 minutes, his movement and willingness to battle for the ball giving Wes Morgan and Robert Huth problems, before he was forced off with a hamstring problem. He drew Kasper Schmeichel into one save down at his near post, having done well to muscle Leicester captain Morgan off the ball.
Coutinho was less threatening with three shots in the opening 15 minutes failing to trouble the goalkeeper, and Lallana wasted his one chance by drilling into the side-netting while Can at least made Schmeichel touch his low effort around the post.
Liverpool's dominance of possession saw much of the game played in Leicester's final third as the Premier League leaders' tried and trusted counter-attacking tactic limited them to fewer chances than usual, with their best chance coming when the in-form Riyad Mahrez's dribble and fierce shot forced Simon Mignolet to tip over late in the half.
That chance came when Benteke lost possession to the much less physically imposing N'Golo Kante and the dynamic certainly appeared to change when Origi's replacement came off the bench.
Benteke looked short of confidence, heading one inviting Henderson cross over on the hour, but reacted instinctively to sidefoot home Firmino's cross after the Brazil international had worked himself some space on the left of Leicester's penalty area having been fed by Can.
It should have been the signal for Liverpool to press home their advantage but Anfield regressed to its anxious, nervous disposition as they dropped deeper and lost composure, even when Ranieri replaced leading scorer Jamie Vardy after a quiet afternoon by his standards.
Substitute Nathan Dyer's deflection was clawed away by Mignolet as the Reds continued to invite pressure on themselves, although Coutinho's effort from distance which skimmed the top of the net or Firmino's angled shot past the far post would have ended that.
The game ended in farcical scenes as Schmeichel came up for a throw-in and Liverpool countered with Can releasing Benteke - in an offside position because of the absent goalkeeper but allowed to continue by a confused linesman - but the striker opted to pass to Alberto Moreno, who was also offside and missed the target anyway.
TWEET OF THE MATCH
@GaryLineker " Huge shock on the cards at Anfield as Benteke gives Liverpool the lead against Leicester." Leicester's unbeaten run finally came to an end.
Simon Mignolet: 6
Nathaniel Clyne: 6
Dejan Lovren: 6
Mamadou Sakho: 5
Alberto Moreno: 5
Emre Can: 5
Jordan Henderson: 7
Adam Lallana: 6
Roberto Firmino: 5
Philippe Coutinho: 6
Divock Origi: 7
Christian Benteke 6
Lucas Leiva: 5
Joe Allen: 5
Kasper Schmeichel: 6
Danny Simpson: 6
Wes Morgan: 6
Robert Huth: 6
Christian Fuchs: 6
Riyad Mahrez: 5
Andy King: 5
N'Golo Kante: 7
Marc Albrighton: 6
Shinji Okazaki: 4
Jamie Vardy: 5
Andrej Kramaric: 5
Leonardo Ulloa: 5
Nathan Dyer: 5
Jordan Henderson - Liverpool's captain was his usual bundle of energy and provided the driving force from a deeper midfield position than usual.
MOMENT OF THE MATCH
Benteke's first-time sidefoot shot from 12 yards to break the deadlock having endured a difficult time after coming off the bench in the first half.
VIEW FROM THE BENCH
Jurgen Klopp was less animated than usual and looked to have made the right call in selecting Divock Origi ahead of Benteke until injury curtailed that plan. Claudio Ranieri, possibly mindful of the impending visit of Manchester City, substituted both in-form players Jamie Vardy and Riyad Mahrez while they were still looking for an equaliser.
MOAN OF THE MATCH
Linesman Stuart Burt got caught up in the added-time panic created by goalkeeper Kasper Schmeichel's decision to go upfield in search of an equaliser and failed to flag for offside when Christian Benteke countered despite there being only one Leicester player in their half.
WHO'S UP NEXT?
Sunderland v Liverpool (Barclays Premier League, Wednesday December 30)
Leicester v Manchester City (Barclays Premier League, Tuesday December 29)