Newcastle started better, with Anthony Gordon testing Caoimhín Kelleher inside the first 60 seconds before Alexander Isak’s cross found no-one in the six-yard box.
Arne Slot’s men attacked again and Alexis Mac Allister was just inches away when he hit the post with a shot from the edge of the area.
Jacob Murphy then copied the Argentine minutes later by hitting the stick on the counter as the match swung back and forth.
The game had briefly lulled, but Isak broke it wide open with a thumping effort from distance to catch Kelleher completely off guard and send the Magpies a goal up.
A tame effort from Gordon and a fizzing shot from Murphy provided opportunities for a second, but Newcastle failed to capitalize on their chances to double their lead against a ragged Liverpool side.
But the Reds came out after the break determined not to give ground to their title rivals and Curtis Jones delivered with an unexpected goal.
Mohamed Salah once again remembered his class with two goals and an assist
Newcastle started better, when Alexander Isak scored from outside the area.
Arne Slot looked to extend his team’s fantastic streak and lead the table
Anthony Gordon left Joe Gómez on the field to give Newcastle the lead again
Mohamed Salah found the Englishman with a clever cross from the right and he fired the ball into the roof of the net.
Liverpool were flying at the time and the Egyptian launched a fierce ball across the box which Darwin Núñez somehow failed to touch.
But the Magpies bounced back, this time with Isak becoming provider. The center forward passed Gordon and the England star turned sharply around Joe Gómez, leaving the center back on the grass and scored.
Isak thought he had put the game out of Liverpool’s reach moments later, cutting in from the right and scoring the third, but the shot was disallowed for a clear offside.
And they were soon made to pay when Joelinton carelessly gave the ball away in his own half and when substitute Trent Alexander-Arnold found Salah diving into the box, the winger made no mistake to level things up.
The Egyptian, unfazed by his uncertain future at Anfield, then provided another fascinating reminder of his importance to the Reds with a clinical finish that gave them the lead for the first time.
Bur Newcastle provided a sting in the tail when Fabian Schar escaped towards the back post with a free kick to slide the ball home after Kelleher completely misjudged the flight.