Richarlison's early strike and Gylfi Sigurdsson's penalty handed Everton their first win at Anfield since 1999 as they banished Jurgen Klopp Reds to a fourth successive Premier League defeat.
Liverpool 0-2 Everton.
Liverpool midfielder Georginio Wijnaldum said the Merseyside Derby loss to Everton was “extra painful,” adding that the Premier League champions were the better team.
Jurgen Klopp Reds suffered a fourth successive home defeat a the hands of Carlo Ancelotti’s Toffees on Saturday.
Richarlison opened the scoring in the third minute after latching onto James Rodriguez's through-ball and finishing in the bottom corner.
Everton were the better side in the first half and created better chances, with Seamus Coleman close to scoring the second goal of the game but his diving header was saved by Brazil shotstopper Alisson.
In the second half, the reigning champions went all out but couldn’t find a way through Jordan Pickford - who head impressive throughout the game.
However, Iceland midfielder Sigurdsson eventually wrapped up the glorious victory for Everton from the penalty spot after Dominic Calvert-Lewin was brought down in the box by Trent Alexander-Arnold.
The result puts both clubs level on points, though Everton have a game in hand as they continue their quest for a top-four finish.
Speaking to Sky Sports after the tie, Dutch midfielder Wijnaldum said: "You know what the derby means for the club, the supporters, the players - it means a lot and the loss is extra painful.
"The first goal we conceded, we tried to keep possession when the long ball came instead of clearing it away. In the first couple of minutes you should take less risk, a pass through the defence and they scored. One more chance after that and we were the better team.
"Losing players during the season upset us a lot. We cannot play the victims, we have to deal with the situation and not feel sorry for ourselves. We have to give until the end of the season, it is painful and you could see if on the faces of the players. That is the situation we are in right now and we have to deal with it.
"Winning games in the Premier League is always difficult and the injuries don't make it easier, we still have a squad who can change it around and we have to work harder to change it around."
Liverpool manager Jurgen Klopp added: “The first goal which we have to defend better gave the direction of the game. It was unnecessary. There were plenty of good football moments so we did well from a creative point of view but we had to chase the game and were not clam enough.
“Everton defended deep and full of passion but there were still moments where we were completely free in the box but we didn’t finish.
“In the second half we changed formation a little because we wanted to cause them more problems. Immediately we had big chances. Sadio [Mane] twice in the box and Bobby was twice in promising positions, so we had all these moments.
“The penalty was late and wasn’t really decisive so we don’t have to talk about that too much.
“We could talk about this for an hour in detail and you would realise what you were talking about would be 90% positive but 10% was not and we have to change 10% because it makes the difference result wise."
On Jordan Henderson’s injury, Klopp replied: “It’s in the region of his groin and abductor. It’s not good. It’s how it is. The rest we will know tomorrow."
On Liverpool's form, the said: "We stand here having lost 2-0. I know how important it is. We feel it deep inside. But from tomorrow on I have to use all the good stuff. These good situations are the guarantee that we can change it but the decisive moments we have to change as well."