Early goals from Peter Crouch and Steven Gerrard put the Reds in control.
A header before half-time from James Beattie, the first goal Liverpool had conceded in nine games, gave the Toffees hope, before Djibril Cisse restored the two-goal advantage immediately after the interval.
Beleaguered Everton took the rare pleasure of sitting pretty above Liverpool in the table heading into both derby matches last season, but normal service had been comprehensively resumed on Merseyside in time for the 173rd meeting of these famous old clubs.
The Reds came across Stanley Park seeking a ninth straight win, after eight straight clean sheets. Contrarily, David Moyes' side had suffered three 4-0 defeats in their last seven games, leaving them perilously close to the drop zone.
Hoping to bridge the dam, Moyes opted for a conservative 4-5-1 formation, with Beattie leading the line. Skipper David Weir returned to the side after missing the 4-0 hammering by Aston Villa on Boxing Day.
For Liverpool, Momo Sissoko returned from suspension and Cisse was given a rare start in attack as Fernando Morientes took a rest.
The hosts threatened to do what no other Premiership side had done in 12 hours when Pepe Reina could only parry Tim Cahill's shot through a crowd of players, but in going for the rebound an offside Beattie fired over.
But Liverpool had the lead when Crouch beat the offside trap on 12 minutes to run onto Gerrard's nod through and beautifully round Nigel Martyn - slotting easily into the corner of the net with a quite brilliant finish.
The goal seemed to settle Liverpool, and after a nervy start they began to pass the ball fluently.
After 18 minutes they had a second through their unstoppable skipper Gerrard. Steve Finnan's cross was nodded away by Cahill, but Everton were slow to react when the ball broke to Gerrard, who fired in past an unsighted Martyn from 20 yards.
Everton, although in midfield disarray, did their utmost to fight back, winning several headers in the Liverpool box. Kevin Kilbane and Joseph Yobo both could have done better.
They had a route back into the game unjustly cut off on 38 minutes when a Mikel Arteta cross was nodded home with aplomb by Beattie. But the linesman wrongly ruled the ball had crossed the byline before the Spaniard whipped it in.
Liverpool somewhat curiously opted to sit deep and allow Everton onto them and in turn gain momentum heading into the break. The game's biggest influence, Gerrard, had barely touched the ball in the 20 minutes leading up to the interval.
Beattie eventually got his goal when another header from Kilbane was skilfully touched into his path by Simon Davies. Finally Reina was beaten.
However, the momentum was killed 80 seconds into the second half when Cisse latched onto Harry Kewell's knock, to easily beat Weir and squeeze the ball past Martyn from a tight angle.
It's a goal that may well save his Liverpool career after speculation he'd be offloaded when the transfer window opens.
From there Liverpool went back into coast-mode and this time the Toffees were unable to respond.
Things just got worse for Moyes when his team lost their best player, Phil Neville, for a second yellow card. After a lunge on Cisse on 55 minutes, Neville mistimed a tackle on Sissoko. It was definitely a foul, but Sissoko certainly made the most of it, endearing him even less to Evertonians.
Beattie blew a golden chance to inspire more hope when he fired over from six yards, before Arteta was collected two late bookings, rather summing up the night for the home side.