A scintillating second-half display from Liverpool, which included goals from Andy Robertson and Divock Origi, helped the Reds narrow the gap to Manchester City to just a single point at the top of the Premier League.
After a frustrating first half at Anfield, Robertson was on hand to nod home Mohamed Salah's cross just after the hour mark. Before Origi sealed the three points with five minutes remaining courtesy of his sixth derby goal.
The victory sees Liverpool remain on the coattails of Pep Guardiola's men as the season's finale edgers ever closer, with supporters none the clearer on who will be lifting the highly-coveted Premier League title in just three weeks' time.
For the blue half of Merseyside, the defeat - their 19th of the campaign - sees them remain 18th in the Premier League, two points from safety with the visit of Chelsea up next for Lampard and co.
Story of the match
Liverpool made two changes to the side that comfortably dispatched of Manchester United just five days earlier.
Captain Jordan Henderson was replaced by Naby Keita who was given the role of partnering Fabinho and Thiago; making up the same midfield trio that wiped the floor with Manchester City at Wembley last weekend, and Benfica earlier this month.
Everton were also forced to make a handful of changes from their 1-1 draw with Leicester in midweek.
Fabian Delph dropped to the bench in place of Abdoulaye Doucoure, Mason Holgate replaced the injured Yerry Mina and, at the eleventh hour, just before the kick-off, Michael Keane was called in to deputise for Ben Godfrey who had sustained an injury in the warm-up.
If the previous 239 editions of this fixture had taken on huge importance, this was arguably in a league of its own given the contrasting fortunes of both sides and their corresponding aspirations between now and the end of May.
And if the pressure needed cranking up at Anfield anymore for Everton, Burnley’s slender 1-0 win at Turf Moor earlier in the day condemned the visitors to the relegation zone before a ball had been kicked at Anfield.
With the Clarets' earlier victory at the forefront of Everton's mind, it was no surprise to see Lampard instruct his side to try and stifle the Reds’ attacking quality with a low block early on. As Mohamed Salah found it increasingly difficult to carve open any space down the right-hand side.
Those early tacts from the Blues were complemented by those - none more guilty than Jordan Pickford - stalling time at every opportunity, ferociously winding up those packed inside Anfield.
Liverpool toyed with Everton on the ball but struggled to work an opening for Diogo Jota, who cut a frustrated figure during a cagey first half.
It was in fact his teammate Sadio Mane who had the best opening of the first 45 minutes, which came as he attempted to catch Pickford out from 25 yards out with a speculative effort.
But despite Liverpool boasting an astonishing 87% possession during the first-half, they were unable to find a way through Everton’s resilient back-line.
The game seemed to explode into life just before halftime as Richarlison's ongoing antics and theatrics were finally ignored by referee Stuart Atwell, which ignited a clash between old foes Lampard and Klopp.
But as Atwell refused to halt play for the Blues’ number 7, who was trying to convince onlookers that he was in fact in need of treatment, Docoure took it upon himself to have multiple swipes at Fabinho before eventually bringing down the Brazilian in the middle of the park. Which resulted in a 21-man brawl.
As both Brazilians lay in a heap on the sun-kissed turf, both sets of players became involved in a tussle. And somewhere in the middle of the uproar, Sadio Mane appeared to poke Mason Holgate in the face.
Atwell waved yellow cards in the direction of both offenders - Doucoure and Mane - in what was the last act of a rather featureless first half.
While Everton knew any potential point wouldn’t have been enough to lift them back above Burnley, it would have been sufficient enough to derail their counterparts’ hopes of securing a second league title in three years.
And with that in mind, Klopp’s men raced out of the blocks after the interval and added extra zip and purpose to each pass as they hung around the Everton penalty area looking for any potential openings.
That allowed Lampard's men to try their chances on the break as the Blues looked to catch out the Reds' infamous high defensive line snoozing.
And After flying down the left-hand side, Gordon thought he had done just that when he was bundled to the ground by Joel Matip. Though Atwell was once again uninterested, despite the pleas from the visiting bench.
The threat of having the three points undeservedly snatched away by those in blue caused Klopp to act swiftly with a double change, as he called upon the supporting cast of Origi and Luis Diaz as the clock hit the hour mark.
And that seemed to inspire that breakthrough the Reds desperately yearned for, as just 60 seconds later the Kop was in raptures thanks to Robertson's first Kop-end goal.
It was Scot's first derby goal, and perhaps the most important of his Liverpool career to date, as he was on hand to nod home Salah’s perfectly-weighted cross.
That cued bedlam at Anfield as the decibel metre cranked up once more.
Everton’s gameplan hadn’t just been ripped up, but it had been shredded by those in Red, who were growing in confidence with every passing minute.
Everton had half-chances of their own, with teenager winger Gordon continuing his role as their most threatening outlet. Demari Gray fired one just a whisker wide of the top corner as those packed inside Anfield had their heart's in their mouths.
Origi put the game beyond doubt five minutes from time when he was well-positioned to convert Diaz’s spectacular overhead kick from close range to seal three vital points for his side, in what is likely to be his last Merseyside derby.
Liverpool XI: Alisson, Alexander-Arnold, Matip, Van Dijk, Robertson; Fabinho, Keita, Thiago; Salah, Mane, Jota.
Everton XI: Pickford, Coleman, Keane, Holgate, Mykolenko, Doucoure, Allan, Iwobi, Gray, Richarlison, Gordon