Jurgen Klopp’s men had a chance to open up a sizeable gap between themselves and second-placed Manchester City after the reigning champions were defeated 2-1 at Newcastle on Tuesday.
And, while the Reds enjoyed a great start at Anfield thanks to Sadio Mane’s early strike, Leicester came back to secure a share of the spoils with Harry Maguire scoring on the stroke of half-time.
Both sides had good chances throughout to secure maximum points but they ultimately had to settle for a share of the spoils.
It moves Liverpool five points clear on 61 points, while Leicester sit in 11th spot on 32 points.
Liverpool boasted two changes from the 4-3 victory over Crystal Palace last time out as Georginio Wijnaldum and Xherdan Shaqiri came in for Fabinho and the suspended James Milner.
Jonny Evans, Marc Albrighton and James Maddison came in to replace Danny Simpson, captain Wes Morgan and Harvey Barnes as Leicester made three changes to the side which lost 4-3 at Wolves on January 19.
Liverpool enjoyed a dream start when they went ahead in the third minute as Sane exchanged passes with Roberto Firmino on the left edge of the area before curling a wonderful right-foot strike into the far corner of Kasper Schmeichel’s net.
Firmino went close to doubling the lead on six minutes when he took control of a ball upfield, got the better of Ricardo Pereira and forced Schmeichel into a superb save at full stretch.
Leicester managed to prevent Liverpool adding any further goals after their relentless start and they should have been level on 25 minutes.
Alisson’s attempted clearance was blocked and Albrighton floated the ball back into the area towards the unmarked Maddison who somehow sent his header wide from six yards with the goal at his mercy.
Mohamed Salah then had a couple of penalty appeals correctly waved away as he twice went to ground under challenges from Maguire in the space of a minute seven minutes before half-time.
Liverpool looked to be heading into the break with a slender lead when they were rocked by a Foxes equaliser in stoppage time.
The hosts failed to fully clear a free-kick into the area and when the second cross came in, Maguire was left unmarked a couple of yards out at the back post to finish calmly past Alisson.
Leicester had two great chances to get their noses in front after the break with Maddison picking up a reverse pass from Ben Chilwell inside the area, but his effort from a tight angle dropped the wrong side of the far corner.
And, on 52 minutes, Maguire headed a free-kick back into the middle from the back post towards Evans who saw his shot brilliantly blocked by Firmino and then Alisson blocked the rebound before Virgil van Dijk finally cleared the danger.
On 57 minutes Liverpool had a shout for a penalty when Naby Keita went down under a challenge from Ricardo inside the area, but referee Martin Atkinson was having none of it despite contact being made.
On 67 minutes Demarai Gray played in Chilwell down the left and his low cross into the middle was inches away from the boot of Jamie Vardy in front of goal.
Gray then went through and instead of looking for the waiting Maddison in acres of space, he went for goal himself and Alisson got down to make a routine stop.
At the other end on 74 minutes it was Firmino who found space for a shot after weaving his way into the box, but Schmeichel pulled off a vital save to keep the Foxes on level terms.
Liverpool finished the game the stronger of the sides as they were desperate for a winner to fully capitalise on City’s slip-up 24 hours earlier, but Hamza Choudhury put in a timely tackle to prevent Mane from bursting clear into the area and Daniel Sturridge curled his follow-up effort over the top.
Mane then sent a stoppage time header over the top at the back post as the Reds had to settle for a point.