Liverpool striker Daniel Sturridge scored two and missed a penalty but it was captain Steven Gerrard who dictated the tone of the 222nd Merseyside derby as Everton were blown away in a scintillating first half.
The England skipper had endured a miserable 45 minutes on his last appearance on this ground against Aston Villa 10 days ago but he rarely does not turn up for a cross-city clash.
He duly led from the front and his influence plus Liverpool's superior firepower meant the Toffees never stood a chance.
Gerrard's header opened the scoring in the 21st minute and was followed by Sturridge's two in quick succession with Luis Suarez scoring his 23rd of the season just after half-time.
Suarez and Sturridge now have 36 Premier League goals between them and remain the most crucial factor in Liverpool regaining their place among Europe's elite.
They helped lift some of the gathering gloom over the club's failure to strengthen in the January transfer window with exactly the sort of performance to give a much-needed shot in the arm to their Champions League qualification challenge.
It was not supposed to be like this for Everton as, following the 3-3 draw at Goodison Park in November and with their rivals in the top four by only a point, this was billed as the closest derby for years and the Toffees' best chance of ending their 14-year run without a win at Anfield.
Everton manager Roberto Martinez had taken his team to Old Trafford and won for the first time in 21 years last month but facing the old enemy on their own turf proved a different prospect.
They came with the idea of imposing themselves and Ross Barkley, back 24 days after breaking a toe, blasted wide after just 64 seconds.
Everton dominated the early possession but it was the hosts creating the chances with Jordan Henderson, Sturridge and Suarez, twice, denied by goalkeeper Tim Howard.
The less prolific of the trio - Raheem Sterling - should have put his side ahead when Sturridge's brilliant ball juggle and lobbed pass put him through but finishing is still an area the teenager needs to work on and Howard saved with his legs.
Liverpool's deadly strikeforce only allow you so many chances but the all-important breakthrough came from the captain in the 21st minute.
Suarez whipped in a corner and the England midfielder cleverly lost marker Gareth Barry to power home a near-post header which James McCarthy on the line could not keep out.
Gerrard wheeled away to celebrate with Suarez and that prompted some items to be thrown from the section of visiting fans in the Anfield Road end.
It was to prove a double blow for Everton as Barry's attempts to re-engage with Gerrard at the corner saw him clatter into team-mate Romelu Lukaku, resulting in the striker being carried off on a stretcher.
Phil Jagielka forced Simon Mignolet into a good save and Kevin Mirallas fired wide but the momentum was all with the hosts and Coutinho's diagonal pass sent Sturridge sprinting from the halfway line and his pace took him well clear to clip past Howard.
If that was clinical his second, less than three minutes later, was brilliant as from Kolo Toure's long ball forward he hooked a lob almost over his shoulder to easily beat Howard.
For all the talk of Liverpool's creaking backline - with four first-choice defenders out injured - they coped easily with an Everton attack now missing Lukaku although Toure had to produced a great recovering tackle to force Mirallas wide and Mignolet saved at his near post.
Everton needed a positive start to the second half but, having replaced Steven Pienaar with Leon Osman, blew it five minutes in.
Jagielka's misjudgement on the halfway line gave Suarez the minimal opening he required and the Uruguay international raced 50 yards with both Everton centre-backs trailing in his wake to slot past Howard.
Gerrard generously gave Sturridge the chance to complete his hat-trick when Sterling was brought down by the goalkeeper but the England striker ballooned his penalty into the Kop.
To compound his error his greed in front of goal ignited the anger of Suarez, well-placed for the easiest of chances, but there is no doubt this is a partnership which delivers more often than not.
STURRIDGE DEJECTED DESPITE HEROICS
Daniel Sturridge somehow managed to sound disappointed with his efforts after scoring twice to lead Liverpool to a 4-0 thrashing of city rivals Everton at Anfield.
The England striker scored two in as many minutes just after the half-hour mark to put Liverpool 3-0 up, but later missed a penalty and was substituted moments after blowing another chance to seal a hat-trick.
Sturridge was visibly upset as he came off but insisted he was frustrated only with himself and not manager Brendan Rodgers for taking him off.
"I apologise for my reaction," he said on BT Sport. "I was disappointed by missing the penalty and felt I'd let myself down as well as the fans. The hat-trick would have been the icing on the cake and it's unfortunate.
"I was disappointed with myself. It was nothing to do with the manager and I'd like to apologise for my reaction if anybody took any offence. It's not about me, it's about the boys and a great victory."
Captain Steven Gerrard, who opened the scoring after 21 minutes, made the decision to hand Sturridge the ball for the penalty as he wanted his team-mate to experience - as he has in the past - a hat-trick against Everton.
"I take responsibility for that," Gerrard said. "I've scored a hat-trick against Everton and I wanted Daniel to experience that feeling. I'm sure the disappointment will see him strive to do better."
Liverpool thoroughly dominated the game against another team challenging for a top-four place, and Gerrard said they had been inspired by a poor performance in their previous home game, a 2-2 draw with Aston Villa.
"I think it goes back to Aston Villa," he said. "We let the fans down, we let ourselves down and it was our first bad performance of the season.
"We had to get back to our way of playing and being ruthless at home. Every player to a man today was superb."
The win sees Liverpool move within six points of the top of the table, three points clear in fourth of Tottenham who face Manchester City on Wednesday, and staying in that top four remains the Reds' first priority as they seek a return to the Champions League.
"That's our target and it's been our target since pre-season," Gerrard said. "We've got two world class forwards and against anyone we've got a chance."
Everton looked a long way from the form which has kept them in that same Champions League battle so far as they fell four points off Liverpool's pace.
A night which began with Ross Barkley making an early return from the injury list ended with on-loan striker Romelu Lukaku hobbling off, and Roberto Martinez admitted his side were not up to scratch.
"Our performance wasn't anywhere near our level and that's down to a combination of things," he said.
"In the first half we never really had that intensity you need and there are reasons for that. We have too many injuries, and we're bringing players back maybe a little too early.
"We weren't ourselves - we lost possession, we were exposed too often and we conceded the first goal from a dead-ball situation. The only other time we've done that was against Liverpool at Goodison.
"There were too many things that stopped us being ourselves and allowed us to be so naive and exposed. It was nowhere near our standard and we want to move on from this and learn some quick lessons."
Rodgers insisted there was no problem with Sturridge.
"I think he was frustrated because he didn't get the penalty," he said. "A manager can make substitutions for all sorts of reasons - tactical, a player not playing well, and that certainly wasn't the case tonight.
"I always say, however you feel, keep it to yourself and speak to me the next day. I think he was just a little bit frustrated after a missed penalty."
Asked about the importance of the win, Rodgers added: "It's another three points in terms of where we want to go.
"It's a massive victory over rivals close to us.
"If you look at Everton they've only conceded 11 goals away from home before tonight and for us to get four and to maybe have had a few more is very pleasing."