Anthony Gordon’s composed first-half finish broke the deadlock for the Magpies, the forward’s maiden goal at St. James’ Park, before Liverpool captain Virgil van Dijk was sent off minutes later following a last-man challenge, bringing down Alexander Isak on the edge of the penalty area.
Newcastle, however, were unable to convert an all-important second goal, with Miguel Almirón clipping the woodwork in each half, before Núñez, introduced from the substitutes' bench, punished the hosts with a deadly, drilled effort in the closing stages.
The Magpies, who suffered a late 2-1 defeat away at Liverpool 12 months ago, were dealt a further blow in the third minute of stoppage-time as Núñez raced behind the United defence before placing the ball beyond Pope.
Eddie Howe named an unchanged starting XI for the third successive game and faced a Liverpool side eyeing a third successive victory at St. James’ Park.
Trent Alexander-Arnold was fortunate to remain on the pitch in the opening exchanges of the contest as the Liverpool full-back, already booked for throwing the ball away, brought down Gordon on the left flank but referee John Brooks refused to brandish the England international a second yellow card to the frustration of the home crowd.
Joelinton created Newcastle’s opening opportunity in front of goal as the Brazil international latched onto a loose ball on the edge of the penalty area but the midfielder’s bending effort was easily held by Alisson.
Nick Pope, who was sent off in last season's 2-0 home loss against Liverpool in February, was alert to deny Mohamed Salah after the Egyptian forward dangerously cut inside from the right flank before the resulting shot at goal was held by the England international.
In the 25th minute, Newcastle opened the scoring through Gordon’s first goal on home soil. After pouncing on Alexander-Arnold’s mistake, the left winger - who began his playing career at Merseyside rivals Everton - raced through on goal before calmly slotting the ball beyond Alisson in front of a raucous Leazes End.
Three minutes later, Liverpool were reduced to ten men as van Dijk clipped down Isak on the edge of the box, with Brooks dismissing the Dutch centre-back despite a lengthy VAR check and deep protests from the visitors.
Miguel Almirón was unfortunate not to double the Magpies’ lead before the half-time break as the Paraguayan’s stinging effort inside the box was brilliantly pushed onto the crossbar by Alisson before the ball was scrambled clear from the penalty area.
Newcastle began the second-half in positive fashion as Almirón went close to netting a neat team-move involving number of United players, with Joelinton’s cross finding the right winger at the back post but his first-time effort was directed over the crossbar.
The hosts continued their pursuit for a second goal as Sandro Tonali darted down the right wing before the Italian’s low cross into the box was turned out for a corner by the recovering Alexander-Arnold before Bruno Guimarães’ audacious attempt from distance flew wide of the target.
More chances followed for United, with Gordon completing a solo run from the left wing before driving the ball wide whilst Botman’s glancing header from Kieran Trippier’s in-swinging free-kick, was directed past the left-hand post.
Botman produced a vital last-ditch challenge to prevent Salah from a potential equaliser, with the Dutchman alert to the Egyptian’s run in behind the United defence before importantly blocking the forward’s drilled shot.
Almirón went agonisingly close to doubling Newcastle’s lead after completing an impressive run from distance but the South American’s curling effort struck the outside of the left-hand post.
Harvey Barnes, introduced from the bench, went close to making an immediate impact after racing onto Joelinton's through ball but the left winger, caught in two minds to shoot or feed fellow substiute Callum Wilson, saw his resulting shot blocked by Joe Gomez.
In the 81st minute, Núñez levelled for the visitors as the substitute after fortunately latching onto Diogo Jota's pass before, from a tight angle, drilling a low effort into the bottom left-hand corner.
With five minutes of stoppage-time awarded, Newcastle pushed forward for a late winner as Longstaff’s low drive was held by the impressive Allison before, in the 93rd minute, Núñez netted an injury-time winner for Liverpool.
After racing onto Salah’s threaded pass, the Uruguayan striker delivered a fierce effort into the net to the disbelief of the home supporters.
Newcastle United: Nick Pope, Kieran Trippier (c), Fabian Schär, Sven Botman (Matt Targett 87), Dan Burn, Bruno Guimarães, Sandro Tonali (Sean Longstaff 72), Joelinton (Elliot Anderson 82), Miguel Almirón, Anthony Gordon (Harvey Barnes 72), Alexander Isak (Callum Wilson 72).
Subs not used: Martin Dúbravka, Tino Livramento, Jamaal Lascelles, Jacob Murphy.
