After a bright start, Liverpool took the lead inside three minutes when Daniel Agger beat the offside trap to glance home Stewart Downing's cross.
Just 10 minutes later, the away side doubled their advantage. From a long ball, Daniel Sturridge played a one-two with Philippe Coutinho, before squaring it for the oncoming Jordan Henderson to tap into an empty net.
James Perch had a chance to reduce to deficit on 35 minutes, but his header drifted wide of the left-hand post from a good Massadio Haidara cross.
Liverpool wrapped up victory just minutes into the second-half through Sturridge. Philippe Coutinho nicked the ball from Hatem Ben Arfa before scooping it through to the Liverpool striker, who smashed it past the onrushing Rob Elliot.
Sturridge doubled his tally just two minutes later after Jordan Henderson returned the favour of his first-half assist in an almost identical goal.
Fabio Borini, returning to the Liverpool side for the first time since dislocating his shoulder, scored just minutes after coming off the bench.
As Newcastle players became increasingly frustrated, Matthieu Debuchy earned a second booking for a cynical foul on Coutinho.
Henderson's resulting free kick drifted past everyone and nestled into the bottom corner for the midfielder's second goal of the game.
Elliot prevented Coutinho from getting on the scoresheet by tipping his effort onto the bar, as the few remaining Newcastle fans inside the stadium headed towards the exits.
The result leaves Newcastle five points clear of safety with four games left.