These were two teams who considered their personal rivalry to encompass the contest to finish fourth in the Barclay's Premier League, but even if the competitiveness of the fixture was lost to Liverpool's devastating aplomb, it was still a rousing occasion.
Everton, reduced to a makeshift defence by injury, were further diminished by their inability to cope with the home side's front three of Daniel Sturridge, Luis Suarez and Raheem Sterling. If the championships and the European places have tended to be shared out between London and Manchester in recent years, Liverpool is a city that is still capable of housing a game of intensity and feeling, of thrillingly captivating play.
These two teams are forever connected by geography, but the relationship is more complex than that. Liverpool and Everton are currently united by their ambition, since both teams are desperate to finish in the top four and qualify for the Champions League. This derby, so charged already by emotion and historic rivalry, carried a contemporary edge; it was heightened by their shared intent.
Both clubs sense an opportunity, in what the Everton manager Roberto Martinez has described as a "transition season" with Manchester United and Tottenham Hotspur's form uncertain while new managers seek to impose themselves. For Liverpool, returning to the Champions League will vindicate Brendan Rodger's rebuilding, and continue the upward momentum of a club that is regaining its sense of pride and self-assurance.
At least in terms of financial strength, Everton are outperforming expectations, but Martinez is a manager of shrewd ingenuity and so this meeting of old rivals, with fresh incentives, was an intriguing encounter. It bristled with meaning, even if there was still a sombre reflection.
Steven Gerrard revealed the day before the game that he had donated £96,000 to the Hillsborough Family Support Group, a cause that he is close to not just as captain, and icon, of Liverpool, but because his 10-year-old cousin, Jon-Paul Gilhooley was the youngest of the 96 victims at Sheffield Wednesday's stadium in 1989.
Gerrard had been reluctant to publicise his gesture, but he felt it was necessary to bring the topic back to the forefront of the public domain. Two investigations are still ongoing, while a new inquest will begin in March. On the eve of a derby, with Everton and its fans having been hugely supportive of the campaign for justice - the events of that terrible day united a city that cherishes the bonds that tie its people together - Gerrard felt the timing was right.
Against that backdrop, the intricacies of the game seemed inconsequential, but then nothing can relate to that appalling loss of life. Football, in its passions and its meaning, runs deep in the city, though. Perhaps, then, it was in some ways fitting that the most towering early contribution came from Gerrard. His header, strong, determined, unflinching, from Suarez's corner set the tone.
Liverpool then swamped all over the Everton defenders and midfielders, robbing them of space, time, and composure. They hared into attack at every opportunity, with Suarez, Sturridge and Sterling proving uncontainable. The home side added to their lead when Coutinho's style and grace under pressure allowed him to slip a ball in front of Sturridge, who then dinked a shot over Tim Howard, the Everton goalkeeper.
The finish was precise and clever, but still not the best of the striker. Two minutes later, he beat Everton's static defence and chased after Kolo Toure's long ball upfield, With a quick glance, Sturridge sized up the situation then, with his back to goal, lifted a volley over the on-rushing Howard and into the corner of the net. The worst of Sturridge was still to come, though, since he blazed a second-half penalty over the bar after Howard brought down Sterling.
Yet Liverpool were in complete command by then, with Suarez having added a fourth soon after the break. Phil Jagielka's loose pass just inside the Liverpool penalty area sent the ball straight to the Uruguayan, who raced upfield before steering a shot beyond Howard.
The occasion, that had promised a potential contest of equals, delivered instead an emphatic performance from Liverpool. Their opponents could only reel, while the outcome allowed Liverpool to still hold on to the belief that they can figure in the Barclays Premier League title race.