The game was put beyond doubt when Sigurdsson calmly hit home after fellow substitute Dominic Calvert-Lewin was felled inadvertently in the area by Trent Alexander-Arnold, who had chased his fellow England international half the length of the field before falling to the floor, after Alisson had saved the striker's effort.
Everton are now level with their sixth-placed rivals on points, whose misery was compounded by skipper Jordan Henderson going off with a left leg injury in the first half.
Richarlison of Everton celebrates with teammates Seamus Coleman, James Rodriguez and Abdoulaye Doucoure after scoring his team's first goal during the Premier League match between Liverpool and Everton at Anfield on February 20, 2021 in Liverpool, England
Image credit: Getty Images
TALKING POINT – Has Carlo found Everton's best system?
Carlo Ancelotti's tactical know-how should never have been doubted and he deserves a lot of credit for the way his defensive set up of three at the back - comprised fully of Englishmen - made things so difficult for the home side.
Michael Keane, who could easily have been man of the match, was a dominant force at the heart of his defence and he was helped out by Mason Holgate and Ben Godfrey on either side.
The athleticism and fluidity offered by those flanking Keane, who are both comfortable at full back, enabled Everton to mostly keep Liverpool at bay and with Tom Davies and Abdoulaye Doucoure in front of them any team would find them hard to break down.
This formation also gets the best out of Lucas Digne at left wing-back giving him freedom to go forward and making him harder to pick up.
Although Liverpool are in far worse form than Manchester City, this formation seems a much better way of dealing with the best teams in the Premier League.
It will be interesting if Ancelotti retains it going forward.
Richarlison of Everton scores his team's first goal during the Premier League match between Liverpool and Everton at Anfield on February 20, 2021 in Liverpool, England
Image credit: Getty Images
MAN OF THE MATCH – Jordan Pickford
The England number one was the villain of the last derby when he ended Virgil van Dijk’s season (admittedly Everton fans might not have thought this way).
With an error gifting a goal to Divock Origi also fresh in the memory, he owed Everton a good performance in a Merseyside derby and this certainly was one.
He was dominant in the air and made key stops from Jordan Henderson and Georginio Wijnaldum’s long-range efforts and spread himself to deny Mo Salah when the Egyptian looked set to equalise in the second half.
He has put his national team status in some doubt with under par peformances this term but this was certainly a display worthy of that position.
Liverpool: Alisson 6; Alexander-Arnold 7, Henderson 7, Kabak 5, Robertson 6; Wijnaldum 6, Thiago 6, Jones 5; Salah 6, Mane 6, Firmino 6. Subs: Phillips 6, Shaqiri 6, Origi 6.
3’ GOAL! Lovely through-ball from Rodriguez and Richarlison makes no mistake slotting the ball past Alisson.
20’ Great save from Pickford. The ball sat up invitingly for Henderson to volley at goal and he hit a perfect effort dipping towards Pickford's right but the England goalkeeper was equal to it.
34’ Fine stop by Alisson. A lovely cross from Digne and Coleman of all people came in from the right flank to meet it with a diving header but the Brazilian keeper pushed the effort away.
53’ Great challenge from Keane. Robertson squeezed the ball past the centre back through to Mane but Keane stretched his leg out to deny the Senegal striker.
70’ Shaqiri makes a nice little pass to Salah in the area and Pickford came out to smother his effort. A great stop from the England number one, who for the first time in a while is justifying that status.
81’ PENALTY! Richarlison got free on the break and set free Calvert-Lewin whose effort was stopped by Alisson but Alexander-Arnold who was prone on the floor after chasing the Everton striker 60 yards inadvertently tripped him over. The referee briefly checks the award and then confirms his decision.
83’ GOAL FOR EVERTON! Sigurdsson calmly finds the corner to Alisson's right. Surely Everton have ended their Anfield hoodoo.