It was a windy night at Anfield, with Liverpool starting the game playing with the wind and hoping to make a fast start against their bitter rivals.
However, it was Carlo Ancelotti's side that made the breakthrough early on as James Rodriguez's through ball caught Ozan Kabak off guard, with Richarlison finding his way in behind and slotting past Alisson in goal.
Liverpool initially struggled to keep much of the ball but a flurry of strikes from outside the box saw them gain more possession as the half wore on, although they were massively ineffective in possession.
Jordan Henderson was forced off with a suspected groin injury as Nathaniel Phillips came on to partner Kabak in defence. The Blues came close to doubling their advantage just before the break via a Seamus Coleman header, but it remained 1-0 at the break.
Liverpool were largely better in the second half but despite a couple of Sadio Mane headers in the early exchanges, they failed to create any clear-cut chances.
Everton were awarded a penalty inside the final ten minutes as Trent Alexander-Arnold was harshly adjudged to have brought Dominic Calvert-Lewin down, with Gylfi Sigurdsson rolling the spot-kick past Alisson to seal a 2-0 win for the Blues.
The result means Liverpool have now lost their last four Premier League games - and their last five at Anfield - which sees their place in the top-four in real jeopardy as Everton, now level on points, look to move above them into sixth.