In an unexpected start to the game, Jonjo Shelvey put the visitors ahead, after a poor clearance from Thiago fell to the former Red and he fired past Alisson from the edge of the box.
Liverpool weren't behind for long after Diogo Jota equalised in controversial fashion.
Isaac Hayden was down inside the box with a head injury after a corner and, less than a minute later, Jota fired past Martin Dubravka at the second time of asking, with Hayden still down in the six-yard box.
Mo Salah then put the Reds ahead and, after Sadio Mane was fouled but managed to stay on his feet, the ball fell to the Egyptian, who made no mistake and put his side in front.
Despite Liverpool starting the game in typical Liverpool fashion - keeping the ball and looking threatening in the final third - it was Newcastle that took the lead.
Allan Saint-Maximin, who is so often the Magpies' creative force, looked dangerous on the counter-attack, squaring up new Reds defender Ibrahima Konate.
He beat his man and, after the ball was played into the box, Thiago's clearance was poor and he practically gifted the ball to Shelvey as if it were an early Christmas present.
Shelvey, who made 69 appearances for Liverpool during his time at the club, then fired past a hapless Alisson in the Reds goal, running away with little celebration.
Liverpool ensured that this wasn't the case for long, creating multiple chances, many coming through Jota.
And it was the Portuguese who equalized and, after his initial header was saved, he fired his second effort past Martin Dubravka.
But there was some controversy over the goal, with two Newcastle players down after the initial corner, and Isaac Hayden still down when the goal went in.
The visiting players weren't happy and Gray could understand why, claiming either the referee or Liverpool should have stopped the game.
He told talkSPORT: "You can understand why the Newcastle players are surrounding Mike Dean, there was two Newcastle players that went to ground.
"But Liverpool won it well, they kept it alive, and Jota stuck ball the ball in the net. If there is a clash of heads, Mike Dean should have stopped the game there and then."
Gray added: "The Liverpool players, let's be honest, should have stopped the game themselves."
And they doubled their tally less than five minutes later.
Shelvey went from hero to villain, as his backpass went straight to Mane and, despite Fabian Schar nearly bringing the Senegalese down, he managed to get a shot away.
It was parried straight to Salah, however, who had the easy job (or so he made it seem) of scoring his 15th goal of the season.
Newcastle were denied a penalty just before half-time, as Ibrahima Konate appeared to kick straight through Joelinton inside the box.
Dean and VAR said no, with Gray stating: "When you're at the bottom of the table, those things go against you. When you're at the top of the table, they go for you."
Liverpool comfortably held onto their lead in the second half.
Alexander-Arnold wrapped the game up with five minutes left, as he struck the ball from 30-yards out and into the top corner.
"What an outstanding finish from Trent Alexander-Arnold," Gray exclaimed.
"He got it out of his feet and rifled it into the top corner. Kevin De Bruyne scored one the other night that was 70mph - I think we've just seen another one."