The writing appeared to be on the wall for Jurgen Klopp's side with only 30 minutes gone, as former Reds youngster Anthony Gordon returned to haunt his former club before Virgil van Dijk was given a straight red card for a last-man foul on Alexander Isak.
However, Eddie Howe's side failed to make the most of their extra player, and a courageous Liverpool side sparked an outstanding comeback through substitute Nunez, who completed the turnaround deep into added time.
Liverpool new boy Wataru Endo was thrown into the deep end on his first start for the Reds, who benefitted from Nick Pope's early red card in last year's win at St James' Park, but they were incredibly fortunate not to go down to 10 men themselves in the opening stages.
After Trent Alexander-Arnold picked up a foolish booking for throwing the ball away, the right-back stopped an effervescent Gordon from charging away on the counter-attack, as the home crowd at St James' Park cried out for his dismissal.
However, seemingly not wanting to make a rod for his own back early doors, John Brooks opted to give Alexander-Arnold a talking-to rather than a second yellow, much to the Magpies' dismay.
Joe Gomez had already been sent out to warm up following Alexander-Arnold's nightmare start, but Klopp held off on making an early unenforced change - a decision he may have regretted for a short period.
With 25 minutes gone, Alexander-Arnold allowed Mohamed Salah's backpass to roll underneath his studs, and one-time Liverpool youngster Gordon raced through to slot home through Alisson Becker's legs.
The on-field bedlam was not over by any stretch, though, as only three minutes after Gordon's opener, Brooks did brandish the red card to Van Dijk, who was sent off for denying Isak a clear goalscoring opportunity.
Van Dijk had more than a few choice words for the officiating team before begrudgingly heading down the tunnel, and Klopp eventually bit the bullet and introduced Gomez, taking off a perplexed Luis Diaz.
It was backs against the wall for Klopp's men following that frenetic half-hour, and it took a spectacular save from Alisson to deny Miguel Almiron Newcastle's second in the 36th minute, as he showed tremendous reactions to parry the Paraguayan's effort onto the crossbar.
Liverpool nevertheless managed to hold Howe's men to just the one goal in the first 45 and did enjoy some forays into Newcastle territory early in the second period, with Sven Botman required to produce a last-ditch block to deny Salah from close range in the 68th minute.
Pope remained untroubled in between the sticks, though, and Almiron very nearly doubled the hosts' lead in the 76th minute, but his curling strike clipped the post after a wonderful solo run.
Eventually, Newcastle's inability to kill Liverpool off would prove fatal, as only a few minutes after being introduced, Nunez capitalised on a Botman error and levelled with a venomous strike across goal in the 81st minute.
The Reds' equaliser was more than merited given the nature of their plucky performance with 10 men, but things would unexpectedly get even better for Klopp's depleted troops, as Salah slipped Nunez through in the third minute of injury time, and the Uruguayan found the bottom corner with a carbon copy of his first strike from the right-hand side of the area.
A shell-shocked Newcastle had no response to the Nunez sucker-punch, as Liverpool snatched the unlikeliest victories from the jaws of defeat, and the Reds have a full week to recover before hosting Aston Villa at Anfield next weekend.
Meanwhile, a dumbstruck Magpies side seek to avoid a third successive loss in the Premier League when they face Brighton & Hove Albion away from home next Saturday.