The Toffees had not won a derby on any ground in 23 previous meetings stretching back to 2010, but took full advantage of the English champions' lost invincibility in front of empty stands.

Victory takes Carlo Ancelotti's men level on points with their local rivals and with a game in hand to come in the battle for a top-four finish.

After a club-record 68-game unbeaten run at home in the league came to an end last month, Liverpool have now lost four consecutive home games for the first time since 1923.

Jurgen Klopp's men remain in sixth, three points off the Champions League places, and suffered another major injury blow when captain Jordan Henderson limped off midway through the first-half with a muscle problem.

The destiny of Liverpool's title defence was irrevocably damaged by the loss of Virgil van Dijk to a knee ligament injury when the sides last met in October.

Van Dijk was in attendance as he continues his rehabilitation, but the gap he has left was exposed inside three minutes.

Season-ending injuries to Joe Gomez and Joel Matip have exacerbated the talismanic Dutchman's absence, forcing Liverpool to recruit two new centre-backs on the final day of the January transfer market.

Ben Davies has still to make his debut, while Ozan Kabak has made a far from promising start.

The Turkish international's lack of pace was exposed in a 3-1 defeat to Leicester last weekend and he was again caught flat-footed when James Rodriguez released Richarlison in behind to fire confidently past Brazilian international teammate Alisson Becker.

Liverpool were furious at the lunge by Jordan Pickford that caused Van Dijk's injury in the previous derby.

The England international has also received plenty of criticism for his performances this season but produced a stunning save to deny Henderson an equaliser from a dipping volley.

Moments later, Henderson, who has deputised at centre-back for the past three months rather than his normal midfield role, added to Liverpool's long list of injuries as he pulled up.

Klopp could only produce a wry smile at the loss of his skipper, but was grateful to his under-fire goalkeeper to not be 2-0 down by half-time.

Alisson made a string of errors with his feet leading to goals against Manchester City and Leicester, but showed why he is still regarded as one of the world's best stoppers with a reflex save from Seamus Coleman's header.

Liverpool responded at the start of the second-half by penning Everton back, but again the Reds cutting edge was missing at Anfield.

Other than Mohamed Salah's penalty in a 4-1 defeat to City, Klopp's men have failed to score in their last five home games.

Sadio Mane planted a header straight into Pickford's arms before the Senegalese was denied by a desperate last-ditch challenge from Michael Keane.

Ancelotti introduced top scorer Dominic Calvert-Lewin for the final half hour on his return from injury.

And the gamble paid off on a rare counter-attack from the visitors as the England international was taken down by Trent Alexander-Arnold after Alisson had saved his first effort.

Sigurdsson kept his cool from the penalty spot to double Everton's lead and sap any lasting belief from Liverpool of ending their losing streak.

G. Sigurdsson

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