Rafael Benitez's side sit two points above the relegation zone and have taken a solitary point from their past seven matches.
It will come as little consolation to a fanbase celebrating the club's 125th anniversary that they played a full part in a pulsating contest, with Joselu having put Newcastle in front in the fourth minute.
Leicester hit back after the early setback, their livewire attack causing Newcastle persistent problems either side of Riyad Mahrez's long-range equaliser.
Demarai Gray handed Claude Puel's men the lead with an hour played, but Dwight Gayle benefitted from a similarly deflected strike to set up a grandstand finish.
Perez was on to try to force a winner for the hosts but tore back desperately as Leicester broke in the 86th minute – his desperate challenge on fellow substitute Shinji Okazaki succeeding only in diverting the ball past helpless goalkeeper Karl Darlow.
GOALLLLLLLLLL! OKAZAKI MAKES IT !— Leicester City (@LCFC) December 9, 2017
(Okay it may have been a Perez og but let's just give it to Shinji and enjoy the moment for now!)
Vardy did well to stay on his feet and find Okazaki as the ball was bundled home. #NewLei pic.twitter.com/vKfahGtfoM
Newcastle fans celebrated the landmark occasion with wonderful crowd display at the Gallowgate end before kick-off and their side responded to a rousing atmosphere by stylishly opening the scoring.
Jacob Murphy produced a glorious pass down the left flank, finding Gayle. Leicester were struggling from that moment and Joselu coolly dispatched his strike partner's cutback.
Leicester might have been left with a mountain to climb but responded by working their way back into the contest and, shortly after Gray fired wide just off target following good work from Vicente Iborra and Jamie Vardy in the 19th minute, they levelled in spectacular fashion.
Mikel Merino sloppily conceded possession in midfield and Mahrez needed no second invitation to drive at a backpedalling home defence and lash into the top corner from 25 yards.
Darlow could have done more to keep out Mahrez's strike but partially atoned for that lapse by saving a Marc Albrighton piledriver.
Leicester's pace on the break was proving troublesome for the hosts and DeAndre Yedlin breathed a sigh of relief when his last-ditch tackle on Vardy did not result in a penalty – replays showing the United States international had got a slight touch on the ball.
Joselu thumped a 52nd-minute header wide from a Matt Ritchie corner but that only seemed to add to a sense of unease around St James'.
The Newcastle faithful's fears proved to be well-founded when Albrighton found Gray with a nicely cushioned lay-off and the winger's shot looped into the top corner via a deflection off Florian Lejeune.
3 - Demarai Gray has scored three goals in seven Premier League appearances under Claude Puel, after scoring just once in his first 50 games in the competition. Spark. pic.twitter.com/r9RFg5ebri— OptaJoe (@OptaJoe) December 9, 2017
A sprawling Darlow denied Mahrez as the Foxes' greater attacking firepower threatened to cause further damage but some poor set-piece defending handed Newcastle a lifeline.
Numerous attempts to fully clear the danger from a 73rd-minute corner proved woefully fruitless and Merino nodded on to Gayle, who cut onto his left foot and beat Kasper Schmeichel via a nick off Harry Maguire.
Gayle had a chance to score the winner when he and Joselu linked pleasingly once more but he dragged wide.
Just as the momentum appeared to have swung back Newcastle's way, Leicester broke from midfield, with Mahrez instinctively picking out Vardy down the left.
The England striker turned the ball inside to Okazaki, whose failure to bring it under control invited Perez's ill-advised bid for heroism.
On balance, an improving Leicester side who are easy on the eye and up to eighth under Puel were worthy of their fortune.