The Blues were celebrating bragging rights after securing their first victory over their Stanley Park neighbours in three meetings and the biggest winning margin for more than 40 years.
Everton ground out the win by maintaining a tough level of play throughout the game.
Luis Garcia tried to set the early pace with a threaded pass to Robbie Fowler, but the veteran striker's soft shot didn't bother Tim Howard.
Everton stepped up the pace though and one heated exchange left Jamie Carragher and Mo Sissoko temporarily floored by the touchline.
Before the game, Blues manager David Moyes talked about Liverpool's superior talent but Tim Cahill and company clearly out-muscled them.
Peter Crouch and new arrival Fabio Aurelio provided the only highlights for the visiting fans during the opening period after linking up well on the left flank.
Rafael Benitez's choice to start Crouch and Fowler may have drawn some criticism. But some clever build-up play nearly saw them on the scoresheet with Fowler's dummy from a Crouch pass providing Aurelio with an opening.
His thundering shot led to a goalmouth scramble as Howard somehow managed to get the ball away from the lanky legs of Crouch.
It was Everton that took the lead following a stunning run by Lee Carsley down the right flank. His pass was deftly flicked on by Johnson to Cahill who tucked away his shot from the edge of the box with ease.
The goal certainly livened up the match as Liverpool tried to respond.
The Reds looked sure to bounce back when Garcia twisted past two blue shirts and unleashed a swerving shot which beat Howard but drifted wide.
But resilient Everton continued to pile on the pressure at the other end. It wasn't long before Merseyside derby new boy Johnson ensured his place in Toffees fans hearts.
Moyes' record signing got an open invitation to score after Carragher made an unforgiveable blunder. The Liverpool-born defender mis-timed his challenge to allow Johnson the chance to slot his shot home under the flailing arms of Jose Reina.
Benitez's pre-match decision to play down the emotions of a Merseyside rivalry didn't pay off. Liverpool came out after the break looking flat and struggled to get back into the game.
The Blues proceeded to push forward and had the visitors on the ropes until Benitez replaced Crouch with Dirk Kuyt on 52 minutes and Fowler with John Arne Riise 10 minutes later.
The fresh legs helped Liverpool crank it up a notch and they even managed to maintain a level of possession inside Everton's half.
Captain Steven Gerrard should have scored after a diagonal pass from Sami Hyypia left him free, but Howard pulled off an impressive save.
But the Reds were done for when Riise twisted his ankle in a rash challenge. He had to be stretchered off with his head in his hands clearly distraught after just returning from ankle ligament damage.
To add insult to injury Reina gifted Everton their third with a howling goalmouth gaffe.
Carsley unleashed a rocket shot from the edge of the area which Reina only managed to push up and backwards into the air. The Spaniard jumped to grab the ball but, realising he would carry it across the line, tossed it straight at Johnson.
The Gladys Street End of Goodison erupted in cheers and laughter as Johnson bagged his second to seal a memorable win.