The Toffees compounded more misery on the Reds as they ended a 24-game winless run on enemy territory.
Everton had a dream start when Richarlison broke the deadlock in the opening three minutes. The hosts did everything to pull parity but their play lacked urgency and the challenge became harder when Jordan Henderson limped off with a groin injury.
The visitors got an insurance goal to protect their lead late in the game when Gylfi Sigurdsson scored from the penalty spot after Dominic Calvert-Lewin was brought down in the area.
“I am very pleased for the club and the supporters. I hope for sure that they are going to celebrate. It was a good performance. A lot of fight and spirit. I am really happy,” Ancelotti said after the game
"We played with two strikers James Rodriguez and Richarlison and we played with [Seamus] Coleman to fix the position of Robertson and four at the back to control [Mohamed] Salah, [Sadio] Mane and [Roberto] Firmino.
“We wanted to avoid the pressure from Liverpool. We know they press a lot but sometimes we had the opportunity to play. Richarlison is back. He is scoring and is playing with a lot of consistency. He has that quality.
“We have to find more consistency at home and we are working on this. We are fighting for Europe and now we are in a good position. This kind of performance helps to improve the belief of the team.
“Jordan [Pickford] did really well. He accepted the criticism. You have to do that and try to be better and he did it.”
