Newcastle 0-6 Liverpool
Liverpool barely missed the banned Luis Suarez during an emphatic win against relegation-threatened Newcastle.
Daniel Agger's looping header and Jordan Henderson's cool finish in the first half set Liverpool on the way to their biggest victory of the season.
Daniel Sturridge scored twice from close range before Fabio Borini poked in his first league goal for the Reds.
Mathieu Debuchy saw red for clattering through Philippe Coutinho and Henderson curled in the subsequent free-kick.
The spotlight had been on Suarez throughout the week, with even Prime Minister David Cameron intervening, saying the striker set "the most appalling example" to children when he bit Chelsea's Branislav Ivanovic last Sunday.
It seems improbable that Liverpool's leading goalscorer, with 30 goals this season and a place on the shortlist for the PFA's Player of the Year award, will not be missed during the next nine games.
But against such obliging opponents as Newcastle, the Uruguay striker's terrier-like qualities were not needed as Coutinho and Sturridge added imagination and spark to Liverpool's attack.
Their manager Brendan Rodgers was dressed all in black for this match, but it is Alan Pardew who will be in mourning as his team suffered their heaviest Premier League defeat at St James' Park.
Pardew had described beating Liverpool as "crucial" - victory against Rodgers' men would have taken Newcastle, who were Champions League contenders last season, to 40 points and, in many people's eyes, safety.
Instead, the Magpies, five points above the bottom three, now have three games - against West Ham, Queens Park Rangers and Arsenal - to secure their Premier League status.
Newcastle's defending will have to improve in the next few weeks as the visitors dominated from the moment Coutinho's beautiful pass set Glen Johnson sprinting down the right inside the opening minute.
Chances fell Sturridge's way before Agger, all alone on the edge of the six-yard box, directed Stewart Downing's lofty cross into the net.
Liverpool quickly doubled their advantage with Coutinho the architect. The Brazilian's precise pass cut through the home defence and Sturridge unselfishly rolled the ball towards Henderson, who side-footed into the far corner.
Only a James Perch header troubled Rodgers's men and a chorus of boos greeted Newcastle's players as they trudged off the pitch at half-time.
Pardew introduced Hatem Ben Arfa and Yoan Gouffran for the start of the second half but the substitutes had little time to make an impact.
Newcastle were unable to cope with Coutinho's directness and it was a magical run and pass from the 20-year-old which allowed Sturridge to score Liverpool's third.
The sight of Steven Gerrard and Henderson combining to beat the offside trap and set up Sturridge for his second, a simple tap in, was enough to make some Newcastle fans leave the stadium with fully half an hour remaining.
It soon got even worse for those Magpies supporters who chose to remain. Borini replaced Gerrard and within 60 seconds the Italian was on the scoresheet.
Downing wriggled beyond Papiss Cisse and found Borini lurking in the box. The striker quickly adjusted his feet before finishing low beyond the diving Rob Elliot.
Newcastle were then forced to play the remaining 15 minutes with 10 men as Debuchy received his second yellow card of the match for a two-footed challenge on the impressive Coutinho.
Henderson stepped up, capitalising on poor defending by curling a free-kick into Elliot's far post, to complete the scoring and maintain Liverpool's hopes of finishing inside the top six.