Substitute Darwin Núñez was the man of the moment, scoring twice from the bench as Liverpool staged an incredible comeback at Newcastle.
The visitors were reduced to 10 men when Virgil van Dijk was sent off just after they had gone 1-0 down in the first half through an Anthony Gordon goal.
However, late substitute Núñez scored his first two goals of the season to seal a memorable victory for the Reds.
Newcastle named an unchanged side from the one that lost at Manchester City last weekend, while Wataru Endo made his first start for Liverpool.
Neither side gave much in the opening stages, with Joelinton and Anthony Gordon forcing Liverpool goalkeeper Alisson into only comfortable saves in 15 minutes.
Liverpool’s best early chance came two minutes later when Luis Díaz forced Newcastle goalkeeper Nick Pope into a save at his near post after a brilliant run.
The deadlock was broken in the 25th minute thanks to a huge error from Liverpool defender Trent Alexander-Arnold, who mis-checked Mohamed Salah’s pass straight into the path of Gordon.
The former Everton winger made his way on goal and slotted past Alisson for his second Premier League goal for Newcastle.
And things got worse for the Reds when defender Virgil van Dijk was sent off for bringing down Alexander Isak on the edge of the penalty area.
Joe Gomez had already come on to replace Díaz, but Newcastle almost extended their lead when Miguel Almirón’s stunning strike was somehow kept out by an even more stunning Alisson save.
Newcastle cautiously went in search of a second goal in the second half, Gordan flashing a shot wide before Sven Botman headed close.
Botman was involved again moments later at the other end when substitute Diogo Jota slipped in Salah, but the Dutch defender made a superb effort to snuff out the chance.
Almirón then came close to scoring again when he unleashed a thunderous strike from outside, but this time Liverpool came to the rescue.
And St James’ Park were stunned moments later when Liverpool substitute Darwin Núñez equalised. The Uruguayan raced on goal after Botman failed to latch on to Jota’s pass before firing low off the post for his first goal of the season.
Remarkably, Núñez didn’t stop there and found himself in goal again in the break. The 24-year-old again finished brilliantly to win the match in dramatic style
Newcastle player ratings (4-3-3)
GK: Nick Pope – 5/10 – Wasn’t tested for large parts of the game given Liverpool’s lack of creativity.
RB: Kieran Trippier (c) – 7/10 – A good outlet on the right and always looking to move the ball forward.
CB: Fabian Schar – 6/10 – Liverpool didn’t test him in a traditional sense.
CB: Sven Botman – 6/10 – Made important challenges just as Liverpool were starting to build a head of steam, but it ended up being his mistake that led to the equaliser.
LB: Dan Burn – 6/10 – Managed to keep Salah relatively quiet but it mattered little.
CM: Sandro Tonali – 7/10 – Willing to burst forward from midfield and it caused Liverpool problems.
CM: Bruno Guimaraes – 5/10 – Sloppy turnover in the closing stages handed Liverpool their chance.
CM: Joelinton – 7/10 – Made sure Liverpool knew he was there with a few crunching tackles.
RW: Miguel Almiron – 8/10 – Hit the bar after a wonder save from Alisson and later the post as well, although his radar was a bit askew with a few others attempts.
ST: Alexander Isak – 7/10 – Pace and movement was the reason Van Dijk was sent off.
LW: Anthony Gordon – 9/10 – Knew he had Alexander-Arnold’s number as soon as the right-back was booked and grew in confidence. Took his goal really well and was a constant threat.
SUB: Callum Wilson (72′ for Isak) – 7/10
SUB: Harvey Barnes (72′ for Gordon) – 6/10
SUB: Sean Longstaff (72′ for Tonali) – 6/10
SUB: Elliot Anderson (82′ for Joelinton) – 5/10
SUB: Matt Targett (87′ for Botman) – N/A
Subs not used: Dubravka (GK), Livramento, Lascelles, Murphy
Eddie Howe – 6/10 – Everything looked to be going right. Will be disappointed his team couldn’t finish the job off against 10 players.
Liverpool player ratings (4-3-3)
GK: Alisson – 8/10 – Kept Liverpool in it in the first half after going behind and made other important interventions when Newcastle were pushing for a second.
RB: Trent Alexander-Arnold – 4/10 – An early booking left him vulnerable and could easily have been sent off inside seven minutes for a cynical foul. At fault for Gordon’s opener.
CB: Joel Matip – 5/10 – A tough reintroduction to the Premier League.
CB: Virgil van Dijk (c) – 3/10 – Can have no arguments about his red card. although he certainly tried. It was a rash challenge in the worst area of the pitch to do it.
LB: Andrew Robertson – 6/10 – Not particularly influential but stayed calm under pressure.
CM: Dominik Szoboszlai – 5/10 – One super long-range shot was about the extent of his input.
CM: Wataru Endo – 5/10 – Making his full Liverpool debut after a substitute appearance last week. Not a good day for it.
CM: Alexis Mac Allister – 5/10 – Avoided a suspension for this games thanks to an overturned red card, but couldn’t make his presence or influence felt.
RW: Mohamed Salah – 7/10 – Not his busiest afternoon but in the mix when both goals were scored.
ST: Cody Gakpo – 5/10 – Back up front. Didn’t get the service and saw very little of the ball.
LW: Luis DIaz – 6/10 – Forced a save in the first half but was sacrificed following the red card.
SUB: Joe Gomez (33′ for Diaz) – 7/10
SUB: Diogo Jota (58′ for Gakpo) – 8/10 – Made a significant impact in comparison to Gakpo, changing the course of the game in the final stages.
SUB: Harvey Elliott (58′ for Endo) – 6/10
SUB: Jarell Quansah (77′ for Matip) – 7/10
SUB: Darwin Nunez (77′ for Mac Allister) – 9/10 – Incredible impact off the bench turned the game in Liverpool’s favour.
Subs not used: Kelleher (GK), Tsimikas, Bajcetic, Doak
Jurgen Klopp – 8/10 – On the verge of losing his temper at one stage and somehow avoided a yellow card. But substitutions eventually got his team back into it in challenging circumstances.