The Reds looked to be on course for a 10th successive home win across all competitions when Sadio Mane gave them the lead after only three minutes, but Harry Maguire's equaliser on the stroke of half time ensured that Jurgen Klopp's side dropped points against a team from outside the established top six for the first time all season.
The leaders still extend their lead at the top of the table to five points after seeing Manchester City fall to a shock defeat at the hands of Newcastle United on Tuesday night, but it is still a missed opportunity for the hosts to have taken the title race by the scruff of the neck.
Liverpool saw Man City break the deadlock after only 24 seconds in that match, and the Reds made a similarly quick start by taking the lead inside three minutes.
Mane collected the ball inside the box before jinking into a shooting position and placing a pinpoint finish past Kasper Schmeichel into the bottom far corner.
The Reds may have been wary of how Man City failed to build on such an early advantage at St James' Park, but that did not initially look like being a problem for Liverpool as they came flying out of the blocks, with Roberto Firmino drawing a smart low save from Schmeichel moments later.
Mane then glanced an unmarked header wide from the resulting corner, before Xherdan Shaqiri could not get anything on a dangerous low cross into the box having darted in front of his man.
Leicester did begin to grow into the game after avoiding any further damage during Liverpool's early flurry, though, and the Foxes should have levelled things up after 25 minutes when a mistake from Alisson Becker led to a golden chance for James Maddison, who could only cushion his header wide of the far post.
It was a warning shot for the hosts, though, and the chances dried up in a nip-and-tuck first half until Leicester stunned Anfield with an equaliser in stoppage time.
The Reds initially failed to deal with Maddison's free kick before it was lifted back into the middle by Ben Chilwell, allowing Maguire to steal away from his marker and sweep his finish home from close range.
It was no more than the Foxes deserved for their first-half improvement, and they could have taken the lead five minutes after the restart too when Chilwell found Maddison in a promising position only for the midfielder to look for a teammate when he would have been better off going for goal himself.
Leicester came even closer to a second goal moments later as again Maguire was left unmarked from a free kick, this time turning the ball back into the middle where only a stunning point-blank save from Alisson prevented Firmino from turning the ball into his own net.
It was a close escape for an underpar Liverpool side, but they should have had a penalty five minutes later when Naby Keita was brought down by Ricardo Pereira after a quick one-two with Firmino, only for referee Martin Atkinson to wave the claims away.
The home side's pressure predictably began to grow in the final 20 minutes as they went in search of a winner, but Leicester almost hit them on the break from one such attack when Demarai Gray's low strike was kept out by Alisson when he had an unmarked Maddison screaming for a square pass in the middle.
Liverpool responded with a chance of their own as Firmino almost provided a moment of magic inside the area, ducking into shooting space before drawing a good low stop from Schmeichel 16 minutes from time.
Such moments were too few and far between for the hosts, though, and the closest they came to a winner in the closing stages saw Mane head over from a corner with virtually the last action of the match.
Over the course of the gameweek it is one point gained rather than two points surrendered for the leaders, though, and they will return to Premier League action on Monday night when they take on West Ham United at the London Stadium.
Leicester, meanwhile, have eased the pressure on manager Claude Puel somewhat with this draw, despite results elsewhere seeing the Foxes slip down into the bottom half ahead of Sunday's match against Manchester United.
LIVERPOOL (4-2-3-1): Alisson; Henderson, Matip, Van Dijk, Robertson; Wijnaldum, Keita (Lallana 66'), Shaqiri (Fabinho 67'), Firmino (Shaqiri 67'), Mane; Salah
LEICESTER (4-4-1-1): Schmeichel; Pereira, Evans, Maguire, Chilwell; Gray (Okazaki 84'), Mendy, Ndidi, Maddison (Choudhury 75'); Alrighton; Vardy (Iheanacho 90')