Cody Gakpo scored his first Liverpool goal as the Reds snapped a four-game winless streak in the Premier League by beating Everton 2-0 in Monday's Merseyside derby.
Everton remain without a win at Anfield in front of a crowd since 1999 and the Toffees were undone by Mohamed Salah's first league goal since Boxing Day nine minutes before half-time.
Gakpo has failed to live up expectations since his January move from PSV Eindhoven
But the Dutch international will hope a derby goal proves to be the turning point as he tapped home Trent Alexander-Arnold's cross four minutes into the second half.
Liverpool are still nine points off the top four in ninth, but could cut that gap on Newcastle to six points and with a game in hand to come when they travel to St. James' Park next weekend.
That clash comes just days before Real Madrid's trip to Anfield in the Champions League last 16 and Jurgen Klopp will be hoping he has finally stumbled upon a solution to some of his side's woes in time for another tilt at the European Cup.
Fabinho and Jordan Henderson were restored to the midfield alongside impressive 18-year-old Stefan Bajcetic.
Darwin Nunez's pace was a constant threat up front, while there were flashes of Andy Robertson and Alexander-Arnold refinding their form as an attacking threat from full-back.
But Liverpool's optimism has to be put in the context of facing an Everton side with just one win in 12 games.
That victory came last weekend in Sean Dyche's first match in charge as league leaders Arsenal were shocked 1-0 at Goodison Park.
But Dyche was given a better understanding of the problems he has inherited.
The absence of Dominic Calvert-Lewin due to injury meant just a second Premier League start for Ellis Simms, who was recently recalled from a loan spell at Sunderland.
Everton were still left to rue what might have been had James Tarkowski's header gone in rather than come off the post just seconds before Liverpool took the lead.
Instead, the hosts collected the loose ball and freed Nunez down the left, who squared for Salah to prod into an unguarded net with Jordan Pickford caught in no man's land.
Everton were undone by another swift counter-attack at the start of the second period.
Robertson charged through midfield and found Alexander-Arnold, whose inviting ball across the face of the goal just required a simple finish from Gakpo.
Salah will feel he should have ended the night with a hat-trick as a desperate lunge from Tarkowski deflected an effort from the Egyptian over before Pickford tipped another shot over.
But there was more good news for Liverpool in the sight of Diogo Jota and Roberto Firmino's return from injury off the bench and Virgil Van Dijk's presence as a substitute after six weeks on the sidelines.
