Cody Gakpo scored his first Liverpool goal in the Merseyside derby, securing the Reds' first victory in five Premier League matches and stopping local rivals Everton from moving out of the relegation zone.
TV Info - Broadcasters
In a key moment in the first half, James Tarkowski struck the woodwork from an Everton corner and Liverpool broke away to score a sensational counter-attacking goal just 13 seconds later, with Darwin Nunez bursting down the left flank and crossing for Mohamed Salah.
It was Salah's 100th Premier League goal or assist at Anfield, in just his 104th appearance, making him the third-fastest player in the competition's history to reach a century of goal involvements at a single stadium.
Liverpool then gained full control of the contest four minutes into the second half as Gakpo finished off another fast break, tapping in at the far post from Trent Alexander-Arnold's low cross.
The Dutchman became the sixth Liverpool player to score their first league goal for the club against Everton, and the first since Raul Meireles in January 2011.
There was more good news for the Reds in the closing stages as Jurgen Klopp, who claimed his 250th win as Liverpool manager in all competitions, was able to introduce both Diogo Jota and Roberto Firmino off the bench after long-term injuries.
Liverpool leapfrog Chelsea into ninth place with 32 points, while Everton remain 18th on 18 points, one point behind their next opponents Leeds United.
Top two collide on Wednesday
There isn't a long wait for more Premier League action as the top two teams, Arsenal and Manchester City, go head-to-head in a huge title encounter at Emirates Stadium on Wednesday.
TV Info - Broadcasters
Following City's victory on Sunday against Aston Villa, Pep Guardiola's side have the chance to go top of the Premier League table with victory.
They would leapfrog their opponents courtesy of a stronger goal difference, while Arsenal could go six points clear of the champions and would still have a match in hand.