The Reds were stunned when they fell behind after less than seven minutes through the unlikely figure of Jetro Willems, but a brace from the in-form Sadio Mane ensured that the league leaders would go into the break ahead.
Mohamed Salah then added a third to wrap up the victory with around 20 minutes remaining, continuing Liverpool's perfect start to the campaign and setting a new English top-flight record in the process.
Jurgen Klopp's side are the first to ever win 14 games in a row while scoring more than once in each victory, while they also become only the third team to win their opening five games in back-to-back seasons.
Roberto Firmino's exertions during the international break saw him left out of the starting lineup as Divock Origi came into the side, and Liverpool struggled to find their usual rhythm in the Brazilian's absence.
Even so, Newcastle's opening goal came like a bolt out of the blue when it arrived after only seven minutes, with Willems collecting Christian Atsu's pass before cutting inside Trent Alexander-Arnold and blasting his finish into the top corner - an unstoppable strike which left Adrian no chance.
Liverpool, trailing for the first time all season, looked to hit back quickly as Alex Oxlade-Chamberlain drove forward from midfield before firing a low strike towards goal, only to see the ball fizz a couple of yards wide of the target.
It was a rare sight of goal for the hosts against an obstinate Newcastle defence during the opening 25 minutes or so, with Klopp's side largely forced to settle for half-chances like Mane's header which flew over the crossbar.
The Reds did slowly begin to get more joy as the half progressed, though, and VAR came into the spotlight again shortly before the half-hour mark when Joel Matip appeared to be hauled to the ground by Jamaal Lascelles, only for the video official to uphold the on-pitch decision of no penalty.
Liverpool would not have to wait much longer for their equaliser, though, with Mane again the man to provide the breakthrough when he curled a pinpoint finish into the top corner after being found by Andrew Robertson.
Suddenly the hosts were very much in the ascendancy and Matip had another half-chance shortly after the equaliser, although there was a setback for Klopp on 37 minutes when Origi limped off with injury.
Firmino replaced him and made an immediate impact, showing the sort of guile his side had been lacking in the opening 35 minutes with a through-ball which led to Mane's second goal.
Newcastle goalkeeper Martin Dubravka will be disappointed with his role in it, though, having beaten Mane to the ball but failed to gather it, sending it bouncing back off the Liverpool forward to leave him with a simple finish - his 20th goal in his last 21 league starts at Anfield.
The goal was Liverpool's 100th against Newcastle in the Premier League era, and they quickly went in search of more with Georginio Wijnaldum drawing a save late in the half against his former club.
Wijnaldum was the first to come close in the second half too, collecting Robertson's pass just inside the area before lifting a fine lobbed effort narrowly over the crossbar.
Newcastle were making a clear effort to be more forward-thinking in the second half, though, and a big chance went begging 10 minutes after the restart when Emil Krafth was found unmarked in the box, only to blaze his finish well over under pressure from Virgil van Dijk.
Liverpool quickly went up the other end and threatened a third goal as Firmino slipped a pass in for the overlapping Alexander-Arnold, who ignored Mane in the middle and went for goal himself, being denied by Dubravka.
The full-back then turned provider with a cross which Firmino glanced into the arms of Dubravka, who was atoning for his earlier error by keeping Newcastle in the game.
The shot-stopper also denied Robertson from point-blank range after a delightful scooped through-ball from Firmino before blocking a pass across goal from the Brazilian which would have left Salah with a simple finish in the middle.
Salah did get his goal - and Liverpool's killer third - with just under 20 minutes remaining when he played a delicious one-two with the irrepressible Firmino before carrying the ball past Fabian Schar and sliding his finish into the bottom corner.
Mane was still searching for his first Liverpool hat-trick in the closing stages of the match and glanced one header wide before putting the ball in the back of the net for a third time, although the offside flag was raised against Firmino in the buildup.
The Brazilian lit up Anfield with his tricks throughout a memorable 53-minute cameo and almost provided another sublime assist late on when he flicked the ball into the box, but a mixture of Salah and Alexander-Arnold were thwarted by Dubravka.
Klopp must now turn his attentions to the beginning of Liverpool's Champions League defence, with a trip to Italy to face Napoli awaiting his side on Tuesday.
LIVERPOOL (4-3-3): Adrian; Alexander-Arnold, Matip, Van Dijk, Robertson; Oxlade-Chamberlain (Milner 75'), Fabinho, Wijnaldum (Shaqiri 84'); Salah, Mane, Origi (Firmino 37')
NEWCASTLE (5-4-1): Dubravka; Krafth (Manquillo 67'), Schar (Fernandez 80'), Lascelles, Dummett, Willems; Almiron (Muto 67'), Hayden, Shelvey, Atsu; Joelintonbody check tags ::