Goals from Richarlison and Gylfi Sigurdsson either side of the break helped the Toffees record their first win at Anfield in 22 years. The Reds, meanwhile, have lost four successive home games for the first time in almost a century.
Carlo Ancelotti got his tactics spot on. as an uninspiring Liverpool failed to make an impact on the game. They had their chances, but Jordan Pickford was at his imperious best.
On that note, let's have a rundown of five major talking points from Liverpool's defeat against Everton.
#1 Everton's early strike jolts Liverpool
Quite often, the best of teams tend to ease their nerves in marquee games like a derby and are caught napping.
That's exactly what happened to Liverpool, who were caught unawares by a lively Everton side in the game's opening exchanges.
The visitors won an early corner that eluded everyone in the box. Fortunately for Liverpool, Ben Godfrey failed to punish Liverpool for their sloppy defending.
A few seconds later, the Toffees again took the attack to Liverpool. Abdoulaye Doucoure was especially fabulous in an advanced role for Everton, winning the ball high up the pitch with quick, sharp counter-pressing.
Once he teed up the creative James Rodriguez, the Colombian spotted the perfectly timed run of Richarlison, who got on the wrong side of Ozan Kabak in a flash and fired past Alisson's far post to hand Everton an early lead.
#2 Everton's direct football troubled Liverpool at the back
Ozan Kabak should never have awarded space to Richarlison for Everton's first goal. The Turkish defender switched off for a split second, which allowed his counterpart to run beyond his back and open the scoring.
The win-back from Doucoure and an inch-perfect pass from Rodriguez painted a glossy picture of Everton in the first half.
Liverpool soon eased into possession, covering a lot of ground with speed and committing bodies forward. However, their overload in passing and crossing did not affect the Toffees, who kept their citadel intact.
Doucoure's physicality and Rodriguez's tricky yet assured footwork ensured Everton kept hold of the ball whenever they won it back. With Richarlison getting released in the turnover of possession without much ado, Liverpool failed to deal with a lively Everton attack.
Lucas Digne also joined Everton's forward forays and getting into crossing positions to keep the Liverpool defence on its toes.