Jurgen Klopp's men looked in control in the first half after Daniel Sturridge put them ahead after 68 seconds and Adam Lallana doubled their lead on the half-hour mark, but the club's former manager launched a comeback.
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However, on the field, it was the perfect start for Liverpool when Sturridge scored inside the first two minutes after using his chest to bring down a long ball from Alberto Moreno.
The England international netted his fourth goal in five games by taking a touch and then drilling the ball across goal, into the bottom far corner of the net.
The visitors were shell-shocked and struggled to respond as they wasted numerous corners and despite getting some minutes on the ball, they were unable to create any meaningful chances for the first 20 minutes or so.
Roberto Firmino created an opening for the home side when he fired a shot from the box after Moreno pulled the ball back following an overlapping run on the left, but the Brazilian's effort was blocked.
Sturridge came close to earning a second goal in the first half when he unleashed a 25-yard attempt, but instead of dropping into the centre of the goal, the ball glided just over the crossbar.
Liverpool's domination on the pitch paid off with a second goal on the half-hour mark, and this time it was Lallana who found the back of the net.
The midfielder showed great skill on the edge of the area to curl the ball past Karl Darlow after latching on to a pass from Moreno, who combined well with Firmino in the build-up to the goal.
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There were penalty appeals at both ends within one minute of each other - the first came from Liverpool when Firmino's cross hit the arm of Paul Dummett in the box, and the second from Newcastle when young Connor Randall caught Ayoze Perez while attempting a low headed clearance.
After referee Andre Marriner waved both appeals away, Newcastle improved slightly and Vurnon Anita tried to make things happen by crossing into the box to find Cisse, whose header missed the target but would have been ruled out due to offside anyway.
The Magpies' best chance of the game occurred in the 45th minute when the ball, from a cross, dropped to the feet of Anita, whose first-time shot from a tight angle went over the bar.
After the break, Newcastle showed signs of a comeback when Papiss Cisse headed home, but it was partly down to Simon Mignolet's goalkeeping error.
The Belgian came off his line to meet Anita's cross, but he missed it completely and Cisse was well placed to head the ball into an empty net in the 49th minute.
Shortly after conceding, Liverpool had a second penalty appeal denied after Sturridge went to ground following a challenge from Cheick Tiote, and Newcastle almost scored immediately on the counter-attack.
Cisse laid the ball off to Andros Townsend, who went for glory from the edge of the box, but his attempt went high into the stands at Anfield.
Liverpool weathered a brief storm and looked to have found a third when Firmino tapped it into the net after Darlow palmed away Joe Allen's header, but the Brazilian was rightly flagged offside.
The Merseyside outfit were in trouble from the 66th minute when Colback drew level at 2-2 after unleashing a shot in the box, which ended up past Mignolet after a big deflection.
The move was started by Townsend, who turned on the edge of the area before chipping in a cross. The ball was then nodded down for Colback, who slammed it home.
The visitors had a spell of dominance as they looked to ride the momentum of drawing level, while Liverpool struggled to find that clinical touch in the final third.
The match was end-to-end in the final five minutes, with Newcastle looking dangerous on the counter-attack, but neither side could find the winner.
Newcastle remain in the relegation zone, one point off 17th-placed Norwich City with three games left to play, while Liverpool are seventh, four points adrift of a European spot and have an extra game.