Goals in each half from Tim Cahill and Mikel Arteta sealed the points for Everton, who moved up to 11th in the Premier League standings as Liverpool slipped to second from bottom.
In Sunday’s late game, Manchester City slashed Chelsea’s lead at the top of the table to just two points after two goals from talismanic skipper Carlos Tevez and David Silva secured a 3-2 victory at battling Blackpool.
City, who were outplayed for long periods by their newly promoted opponents, moved up to second place after the victory.
Earlier, Liverpool’s new American owner John W. Henry looked on at Goodison Park as Roy Hodgson’s Reds crashed to their fourth defeat of the season, leaving them with only six points from eight games.
Afterwards a defiant Hodgson denied Liverpool were in crisis despite a defeat which continued their worst start to a season for 57 years.
“I don’t feel it to be a crisis because the way we have played today I don’t think anyone would believe that is the type of football of a team in the bottom three,” Hodgson told the BBC.
“I think we can consider ourselves unlucky.”
Hodgson also defended out-of-sorts striker Fernando Torres, who had another fruitless afternoon in front of goal, saying the Spanish international was still struggling to recover his best form after the World Cup.
“We don’t have any injury problems with him. He got battered for his performances at the World Cup and mentally he is a bit low,” Hodgson said.
“He needs a goal to get his confidence back. I have no qualms with his performance against Everton.”
Everton boss David Moyes meanwhile was satisfied with a result which lifted them clear of the drop zone.
“We are getting away from the wrong end of the table. We are a good enough team to be at the top end,” he told Sky Sports.
“I thought we have played better in the majority of games than we did today but it was a derby and a different kind of game.
“Some of our performances (earlier in the season) were good but we did not get the result but today we did enough.”
A frenetic opening spell saw Everton take the lead on 34 minutes. Irish wide player Seamus Coleman surged down the right and cut back an inviting cross for Cahill, who blasted high into the net past Liverpool goalkeeper Pepe Reina.
The goal was no less than Everton deserved after they dominated a feisty first half that saw referee Howard Webb book three players — Everton’s Cahill and Liverpool’s Maxi Rodriguez and Raul Meireles.
Ayegbeni Yakubu forced a smart low save from Reina shortly before Everton took the lead, while Reina had to be alert on the stroke of half-time to save a rising long-range shot from Leon Osman.
Spanish midfield maestro Arteta doubled Everton’s lead five minutes after the interval, lashing home a swerving right-foot shot from the edge of the area. With the clock ticking down, Torres saw a shot well-saved by Tim Howard but it could not mask another disappointing afternoon for the Spaniard, who also picked up a late booking.
In Sunday’s late game at Bloomfield Road, Blackpool were desperately unlucky to come away empty-handed after a spirited performance where they more than held their own against cash-rich City.
Blackpool forward DJ Campbell had missed a glorious opportunity to put Blackpool 1-0 up before Gary Taylor-Fletcher had a goal controversially disallowed for offside in the second half.
Tevez then fired City into the lead with a superb clipped finish, before Blackpool fought back to level with a flicked header from Marlon Harewood.
Blackpool’s delight at securing an equaliser was short-lived however as Tevez struck again less than a minute later.
There was a whiff of controversy about the goal however with Tevez appearing to foul Ian Evatt in the build-up.
Spanish international Silva netted a sublime third for City on 90 minutes before Taylor-Fletcher hit back for Blackpool to ensure a nerve-wracking final minute of stoppage time for Roberto Mancini’s men.
Blackpool manager Ian Holloway blamed the loss in large part on referee Phil Dowd.
“He’s got three massive decisions wrong, which cost my team against one of the so-called big teams. For me, we could have been one point behind them if things had gone our way, as they clearly should have done.
“We’re getting absolutely bo diddly squat, week in, week out. But there you go, such is life.”
City boss Roberto Mancini was happy to win ugly.
“Sometimes it is important to win like we did today,” the Italian told Sky Sports.
“Today we didn’t play well. It was important at the end that we scored three goals. It is not easy to score three goals away from home.”