Liverpool strengthened their grip on Champions League qualification by effectively ending the top-four aspirations of Everton, whose woeful run in Merseyside derbies continued.
The Blues have not won at Anfield since 1999 - their last victory of any sort in the cross-city encounter was almost seven years ago - and despite lofty ambitions going into the game they never looked like actually ending that sequence.
First-half goals from Sadio Mane and Philippe Coutinho, sandwiched between a debut equaliser for Matthew Pennington, were followed by substitute Divock Origi's clincher to make it 3-1 as Jurgen Klopp extended his 100 per cent derby record to three wins, the only manager in the club's history to do so.
The six-point gap which had given Everton, who had lost once in 12 matches since the December derby at Goodison Park, optimism before kick-off now looks an insurmountable one.
Ronald Koeman, whose argument with Republic of Ireland boss Martin O'Neill over the treatment of James McCarthy saw him sign off his Twitter response 'From the master tactician', was forced to switch to a back three after injuries on international duties but it never looked coherent.
Mane took immediate advantage, starting how he finished at Goodison where he scored an added-time winner, with a superb individual effort after just eight minutes.
Having exchanged passes with Roberto Firmino close to halfway the Senegal international set off on a diagonal run which had defenders backing off enough for him to steer a left-footed shot across Joel Robles, who by favouring his near post left a lot of room to his left.
The Everton goalkeeper was almost further embarrassed when he palmed Coutinho's shot up and onto the crossbar, a warning Everton did not heed when the Brazil international once again cut back onto his right foot to curl a shot inside the same post on the half-hour.
In between Pennington, on his first appearance of the season, had scrambled home Everton's only shot on target in the first half after Liverpool failed to deal with Leighton Baines' corner.
The visitors were fortunate to get the interval with 11 men on the pitch as a pumped-up Ross Barkley somehow managed to escape a caution until the 39th minute when, after two previous reckless challenges, he was lucky to only see yellow having gone over the top on Dejan Lovren, back in the side for the first time since the end of January.
Defender Ashley Williams may yet face retrospective action, however, after appearing to stand on Emre Can in an earlier tussle in an encounter which had the sort of feistiness associated with a fixture which has witnessed 21 red cards in 49 previous Premier League meetings.
Mane's departure to a potential knee ligament injury early in the second half was a major blow for the hosts but any respite for Everton was short-lived as his replacement Origi swept home Liverpool's third with a first-time shot from Coutinho's pass less four minutes after coming on.
Liverpool seemed content with their lead so Everton were given a touch more freedom but teenager Dominic Calvert-Lewin had their last chance and should have done better with his close-range header after Simon Mignolet did well to parry Mason Holgate's deflected shot.A Twitter List by BelTel
SIMON MIGNOLET: Did not command his area at the set-piece that led to Everton's goal but was otherwise solid. 6
NATHANIEL CLYNE: Another steady performance in defence and attack from the England international. 6
JOEL MATIP: Kept a close eye on dangerman Lukaku throughout the game, hardly allowing the Belgian any joy. 7
DEJAN LOVREN: Some may think he overreacted to an admittedly poor challenge from Barkley but defended with authority. 7
JAMES MILNER: Solid display from the ever-dependable utility man, who may offer little flair at left-back but is rarely caught out of position. 6
GEORGINIO WIJNALDUM: Hard-working display from the Dutchman, keeping the Reds moving forward. 6
LUCAS: Played a key role breaking up Everton play on numerous occasions. 6
EMRE CAN: A performance of high energy from the German which saw him make important challenges and have the confidence to get forward. 6
SADIO MANE: Opened the scoring with a superb solo goal and gave Everton constant problems before being forced off injured. 8
ROBERTO FIRMINO: His flicks and quick link-up play with Coutinho did not always come off but Everton struggled to read him. 6
PHILIPPE COUTINHO: Demonstrated his dribbling ability and finishing skill with a brilliant individual goal that capped a fine performance. 8
DIVOCK ORIGI (for Mane, 57): Needed little time to get into the game, curling a shot wide and then lashing in a fine shot from distance. 7
TRENT ALEXANDER-ARNOLD (for Coutinho, 74): Allowed Coutinho to have a rest and even went close to scoring. 6
RAGNAR KLAVAN (for Firmino, 90): Introduced late on as Liverpool played out time. 5
JOEL ROBLES: Was slow to react and out of position for Liverpool's first two goals, although he did make saves from Coutinho and Alexander-Arnold. 4
MATTHEW PENNINGTON: Had a dream derby introduction as he pounced for Everton's goal but otherwise it was a tough introduction to top-flight football for the young defender. 5
MASON HOLGATE: Looked good when getting into forward positions but struggled defensively, notably when Coutinho was running at him. 5
ASHLEY WILLIAMS: A mixed performance from the experienced centre-back, making some timely challenges but also being caught out on occasions. 5
PHIL JAGIELKA: Was overworked having to deal with the likes of Coutinho, Firmino, Mane and Origi. 5
LEIGHTON BAINES: Reliable in his defensive duties but unable to get into the game going forward, except at set-pieces. 6
ROSS BARKLEY: Walked a disciplinary tightrope in the first half and might have had a booking before the yellow-card challenge on Lovren that could have been red. Improved after the break. 5
IDRISSA GUEYE: One of Everton's more accomplished players when in possession, but Liverpool tried to starve him of that. 6
TOM DAVIES: Failed to halt Mane for the opening goal and was unable to make an impression. 5
DOMINIC CALVERT-LEWIN: Largely ineffectual before being withdrawn. 4
ROMELU LUKAKU: Considering the expectation, the Belgian was a big let-down, hardly making any impact. 4
ENNER VALENCIA (for Davies, 66): Tried to give the visitors more impetus but Liverpool retained control. 6
GARETH BARRY (for Pennington, 67): Brought more composure to the Everton midfield for latter stages but could not change course of game. 6
KEVIN MIRALLAS (for Calvert-Lewin, 82): Too late for the Belgian to stage a salvaging act. 5
Captain Jordan Henderson is still not fit to return from a foot problem which has sidelined him since early February.
Striker Daniel Sturridge is training outdoors again after seven weeks out but is still working under the rehabilitation coaches and will not feature.
Squad: Mignolet, Clyne, Matip, Lovren, Milner, Can, Lucas, Wijnaldum, Mane, Firmino, Coutinho. Subs: Karius, Grujic, Klavan, Moreno, Origi, Woodburn, Alexander-Arnold.
Everton will be without Seamus Coleman, James McCarthy, Ramiro Funes Mori and Morgan Schneiderlin for the Merseyside derby against Liverpool at Anfield on Saturday.
The international break was a dreadful one for the Toffees, as Coleman suffered a horrific double fracture to his leg playing for the Republic of Ireland against Wales, team-mate McCarthy aggravated a hamstring problem in the warm-up before that match, and Funes Mori tore his meniscus while playing for Argentina.
Everton boss Ronald Koeman has subsequently revealed that Schneiderlin, who came off in Everton's last game with to a calf injury, will be sidelined this weekend as well.
Squad: Robles, Jagielka, Ashley Williams, Holgate, Pennington, Davies, Gana, Baines, Barkley, Lukaku, Calvert-Lewin. Subs: Kone, Mirallas, Barry, Valencia, Stekelenburg, Lookman, Kenny.
Anthony Taylor (Cheshire)