The leaders couldn't build on a goal after 121 seconds by Sadio Mane at a snowy Anfield, with Leicester equalizing through Harry Maguire in first-half injury time and causing Liverpool problems in the second half.
Only a fine reaction save from goalkeeper Alisson Becker, who turned the ball away after teammate Roberto Firmino diverted it toward his own goal, denied Leicester another surprise win after beating Chelsea and Man City in the past five weeks.
As it was, Liverpool's lead is now five points with 14 matches left as the team looks to win the league for the first time since 1990.
Liverpool's quickest league goal in nearly three years was a 30-pass move that culminated in Andrew Robertson playing the ball across the box, through Firmino's legs, to tee up Mane for a low shot around Maguire's legs and inside the far post.
The Foxes are favored opposition for the Senegal international, who now has had a hand in five goals — three goals and two assists — in his last five appearances against them. It was the 100th goal scored at Anfield by Mane and fellow forwards Mohamed Salah and Firmino.
Firmino and Mane wasted chances before Liverpool's tempo dropped.
Alisson miskicked a short backpass from Jordan Henderson, who was playing as an emergency right back, straight to James Maddison, who went down under a challenge but was not awarded a penalty.
When Alisson delayed another clearance, it was half-blocked by Jamie Vardy, and Maddison made a complete mess of his far-post header when the ball was returned into the box by Marc Albrighton.
Maguire found himself in action at both ends of the field with varying results, as Salah ran into him in the penalty area — with no punishment for either player — before the England defender was booked for tripping Mane as he tried to run clean through onto Robertson's pass.
By far his biggest contribution, however, was the stoppage-time volley when Liverpool failed to clear a free kick. Ben Chilwell returned the ball into the box and Maguire sneaked in at the far post to guide in a finish.
The big center-back almost repeated the feat early in the second half, and it required Alisson to get Firmino out of trouble when his Brazil teammate diverted Maguire's header goalward.
Naby Keita felt he should have had a penalty when, after exchanging passes with Firmino to get through on goal, Ricardo Pereira laid two hands on his back causing him to fall. The referee awarded a goal kick.
While Liverpool was appealing for another penalty, this time on Virgil Van Dijk, Leicester launched a three-on-two counterattack but Maddison was furious when Demarai Gray opted to shoot rather than squaring the ball.
Leicester goalkeeper Kasper Schmeichel denied Firmino with the last real chance of the game, with Mane flashing over a header in added time.
Liverpool's unbeaten home record was extended to 32 league matches but the first dropped points at Anfield since October meant the sense of a missed opportunity was palpable at the final whistle.