The Reds were stunned by a superb early goal from Jetro Willems on seven minutes as Newcastle eyed up another away upset following their win at Tottenham.
Jurgen Klopp’s side are made of sterner stuff, however, and Sadio Mane’s brace had them in front by the interval.
The second half was controlled by Liverpool, though Emil Krafth did pass up a great chance to level at 2-2, with Mohamed Salah slotting the key third goal on 72 minutes to wrap up the points.
Roberto Firmino, off the bench to replace Divock Origi in the first half, showed some sublime touches in the second period, including teeing up Salah for his goal.
The win means Liverpool have won five straight games to begin the season for the second year running, while they have now won 14 on the trot in the league.
Newcastle could scarcely have asked for a better start. A long punt forward was controlled by Christian Atsu and he had time to pick out Willems. The wing-back unleashed a powerful shot across Adrian into the top corner to give the Magpies the lead.
Alex Oxlade-Chamberlain almost levelled soon after but it was Mane’s strike on 28 minutes that restored parity.
He took a pass inside the box from Andy Robertson before curling a shot past Martin Dubravka into the corner of the net.
Firmino replaced Origi and played a role in Liverpool’s second five minutes before the break. Dubravka raced from his line to thwart a through ball towards Mane but his clearance rebounded off the forward, leaving Mane with a simple tap-in.
Newcastle’s best chance to level came on 55 minutes. A cross from the left caught Robertson out and Krafth was able to control on his chest but, with ten yards between himself and the goal, he blazed over the crossbar.
That was to prove costly. Firmino’s sublime footwork allowing him to exchange passes with Salah, before the Egyptian burst into the penalty area and slotted underneath Dubravka to give Liverpool daylight.
Mane had the ball in the net after more set-up play from Firmino, though he was denied the hat-trick by an offside flag.