The Reds were dominant from the off and got an early lead through Mohamed Salah's brilliant turn and strike, but the visitors had encouragement of their own throughout the game.
Jurgen Klopp's side, who were wasteful with a plethora of chances, switched off in the final 20 minutes and were lucky when VAR intervened to rule out Callum Wilson's added-time goal for handball.
But the Reds allowed Joe Willock space to finish as the Magpies made it 1-1 with the final kick of the ball to punish Liverpool - who sit in sixth place in the table.
Liverpool got off to the perfect start inside three minutes as Salah collected a dropping ball inside the box with a superb first-touch and fired into the top corner to leave Martin Dubravka in goal with no chance.
The Reds continued to have the majority share of the ball, but the Magpies looked threatening in bursts, only for the offside flag to come to Liverpool's rescue.
But Sean Longstaff managed to beat the offside trap against a static Reds defence and looked likely to grab an equaliser, only for Alisson to make a good save and deny the Magpies midfielder.
The visitors found the back of the net through the ensuing corner, but the goal was immediately disallowed for a foul by Jonjo Shelvey on Alisson.
Jota had two attempts in quick succession as he looked to double the Reds' advantage, but his first blazed over the crossbar whilst the second went straight into the hands of Dubravka after good work by Mane in the build-up.
Liverpool looked especially vulnerable at the back against the pace of Allan Saint-Maximin, with Ozan Kabak having to remain especially composed after an early yellow card.
A mix-up at the back for the visitors saw Salah win the ball before Jota had a free strike at goal, but the Portuguese forward skewed his effort wide in a real let-off for Steve Bruce's side.
An excellent lofted ball by Firmino saw Salah beat the offside trap and latch on whilst running into the box, but Dubravka was up to the task after a weak shot from the Reds forward.
The chances kept coming for the Reds as Firmino and Jota linked up at the edge of the box, but Jota's shot was disappointing as another opportunity went begging for the Liverpool no.20.
Salah found his way in behind for the umpteenth time and this time the Egyptian cut back and played in the unmarked Mane, who looked favourite to make it 2-0, only for the Reds forward to take too long and give Dubravka the chance to smother the ball.
Mane had another chance but finished wide of the post as the Reds went just 1-0 up into the break, when on another day it could have been 4-3 if not for the unremarkable finishing on display.
Firmino had an early chance in the second half but his shot was too weak to trouble the goalkeeper. Both sides appeared to be set up in the same way to the first 45 minutes, with acres of space for both sets of attackers to exploit.
Alisson was then called into action twice, first crucially beating Joelinton to the ball after he got in behind before then denying the Newcastle forward who looked favourite to score from the edge of the box.
Klopp opted to withdraw Jota just before the hour mark to shore up his midfield with James Milner coming on in place of the 24-year-old, who was heavily involved throughout but didn't have the final ball or composure with his finishing to capitalise.
Callum Wilson and Joe Willock then came on for the visitors, who felt at 1-0 the game could still be turned in their favour in light of the Reds' inability to take advantage of plenty of chances coming their way.
The changes had the desired effect for Liverpool, who were able to dominate more of the ball in the middle of the park and plug the gaps at the back.
Sloppy play at the back from the Magpies handed an opportunity to Mane, who fed Salah with time and space. But the Reds forward dragged his shot wide as the Reds continued to miss the mark in their quest for a second goal.
Trent Alexander-Arnold came close after being set up for a volley by Thiago - who had an influential game - but the right-back's strike went wide of the post.
Liverpool were forced to hang on in the final minutes and it was all drama as Wilson bundled the ball home to seemingly make it 1-1, only for VAR to intervene and rule the goal out for handball.
It was a big let-off for the Reds, but they couldn't hold on for the final seconds as Newcastle had the ball in the back of the net again; this time through substitute Willock, who finished past Alisson after the ball dropped to him inside the box.
The result means Liverpool remain a point behind fourth and fifth-placed Chelsea and West Ham, who play later in the day. It's another missed opportunity for the Reds, who can only blame themselves for their capitulation.
Liverpool XI: Alisson, Alexander-Arnold, Fabinho, Kabak, Robertson, Thiago, Wijnaldum, Firmino, Salah, Jota, Mane.
Next Fixture: Manchester United (A) - 2 May, 16:30 BST