As a reminder that they can win comfortably with Steven Gerrard becalmed, this was critical.
The England midfielder has been hauling the Merseysiders single-handedly through this stuttering campaign in recent weeks, battering goals from distance when he was not busy stifling opponents deep inside his own half, but he was barely required yesterday. For all that Newcastle briefly led, everything about the visitors here was obliging, whether that meant own-goals, defensive mistakes or mindless fouls. Liverpool have been craving such hand-outs.
It means that at Christmas they will be only six points adrift of fourth spot and qualification for next season's Champions League, which Benítez will believe is a manageable margin to make up. That conviction has been given all the more credence now that confidence is flooding back. This was perhaps Harry Kewell's best performance in a Liverpool shirt since he signed from Leeds 18 months ago, his turn away from Jermaine Jenas just after the hour bettered only by a slide-rule pass to Milan Baros.
The Czech, watched by his father and sister in the directors' box and flourishing on a rare appearance alongside another striker, tore away from the dawdling Titus Bramble and Robbie Elliott before rounding Shay Given to roll his side's third goal gleefully into the unguarded net.
"Liverpool probably think that was a marvellous goal but you don't see too many scored in the Premier League that go straight through the centre between two centre-backs," growled the beaten manager, Graeme Souness.
Not that the locals cared. After two wins in the previous eight Premiership matches life is suddenly rosy again in these parts. "We showed character and a good mentality, controlling the game and creating chances," said Benítez, his only concern his side's 10-match sequence without a clean sheet. "I have a squad with plenty of options now and we played six players with offensive mentalities today."
As it transpired, the player with the most offensive outlook was the visitors' Lee Bowyer. Already cautioned for a lunge at Xabi Alonso early in the second period, the former Leeds midfielder crunched into the substitute Florent Sinama-Pongolle 14 minutes from time to prompt a dismissal. There were squealed protests from the one-time England player, an open-armed attempt at innocence, but this was lunging lunacy.
Given that Bowyer had appeared to kick Alonso in the back immediately before his foul on Sinama-Pongolle, he could have no complaints. Souness offered a more honest assessment - "he let his team-mates down" - and, with the visitors reduced to 10, Liverpool's strut should have yielded more reward. Newcastle can count themselves lucky to have been spared a slaughter.
The home side had not always appeared so irresistible. This game had begun as a shapeless stroll, Luis García's wasteful blaze into the Kop from Baros's early wriggle and cross setting a sloppy tone that even Gerrard could not change. Only when Newcastle roused themselves momentarily from their mediocrity did the game spark.
Kieron Dyer's slipped pass found Bowyer down the right, the midfielder's low centre guided into the net by Patrick Kluivert, who had been offside in the build-up but was deemed not to be interfering with play.
The Dutchman should not have been involved at all, having been handed his chance only after Craig Bellamy succumbed to a back injury in the pre-match warm-up, a legacy of an injury sustained against Sporting Lisbon last week. Newcastle should have known then that their luck was never likely to hold.
It did not. Within three minutes parity had been restored, the hapless Bramble heading mystifyingly into his own net under vague pressure from Sami Hyypia from Gerrard's whipped corner. From Liverpool's next attack, prompted by Jamie Carragher, Baros spun away from Elliott, then slipped Neil Mellor into space. The striker's finish was instinctive, his side-footed shot speared across Given and into the far corner for a fifth goal of the season, though the visitors' defence parted with barely a complaint.
García and Antonio Núnez might have added to Liverpool's plunder and Kewell's flash of brilliance killed off the contest. "Harry's played well in the last four or five games," Benítez insisted. "I have a lot of confidence in him and he's playing better all the time. He's training well and he's so important for us." In truth, Liverpool have long been waiting for the Australian to justify his £7m transfer fee and £40,000-a-week wages.
Newcastle gave him licence to excel, their powder-puff defending an invitation to revel in possession. Souness has much to trouble him this morning, his side languishing nearer the relegation zone than the Champions League places, for all that they created chances even in the absence of Alan Shearer and Bellamy.
Jenas missed their most presentable, slicing over the bar after Shola Ameobi had pulled back from the by-line, though Bowyer's absence through suspension at Blackburn on Boxing Day has prompted another headache. Moreover, Souness will realise that his side were battered here with Gerrard content to remain on the periphery.
Therein lies Liverpool's encouragement and perhaps Newcastle's greatest worry.