Early goals from Daniel Agger and Jordan Henderson put Brendan Rodgers' visitors, who moved back to within five points of Everton ahead of the Merseyside derby, on their way to victory in the first game of Suarez's 10-match ban.
And Daniel Sturridge's second-half double followed by a tap-in from the returning Fabio Borini and a Henderson free-kick after Mathieu Debuchy had been sent off further embarrassed Newcastle.
For Alan Pardew's side, it was a devastating, disorganised and disheartening loss amid an ugly atmosphere on Tyneside in the wake of their last defeat by derby rivals Sunderland.
And having been booed off, Newcastle now remain just five points from the relegation zone having played a game more than Wigan Athletic and Aston Villa in the closing weeks of the season.
Liverpool tore at their hosts from the off and needed just five minutes to forge their way ahead when Agger took advantage of lazy defending to run unmarked on to Stewart Downing's lofted cross and head past the helpless Rob Elliot.
Liverpool increased their lead with 17 minutes gone after mounting a flowing attack which left the Magpies floundering again, the excellent Philippe Coutinho sliding the ball into Sturridge's path for him to square for Henderson to double the score.
By contrast, Newcastle had little or no penetration as lone striker Papiss Cisse was starved of possession with Yohan Cabaye and Moussa Sissoko becalmed by a sea of red shirts.
But they should really have been back in it with nine minutes of the half remaining when full-back Massadio Haidara produced the first cross of any note to present James Perch with a free header, only to see him head wastefully wide.
Pardew made his move at the break, replacing Perch and Jonas Gutierrez with Hatem Ben Arfa and Yoan Gouffran, knowing his side needed something different and needed it fast.
Gouffran might have obliged within four minutes when he got his head to Cabaye's cross, but his looping header was easily collected by Jose Reina.
But the game was effectively over in the 54th minute when Ben Arfa, who had shown encouraging signs, was robbed by Coutinho wide on the right and he sped forward to slide in Sturridge, who blasted past Elliot.
But things were to get much, much worse for the Magpies when they were carved open once again when Steven Gerrard and Henderson combined to set up Sturridge for his second with half-an-hour still to play, and the rout was far from complete.
Borini needed just two minutes to find the back of the net on his return from injury as a substitute when he converted Downing's cross, and Henderson sent a 74th minute free-kick across Elliot and into the bottom corner with no team-mate able to get a touch to make it 6-0.
Debuchy got his marching orders after receiving a second yellow for a foul on Coutinho, and only a fine 82nd minute save by Elliot denied the Brazilian a seventh goal as the storm clouds gathered over Tyneside with three games of a difficult campaign remaining.