A James Beattie effort after just 14 minutes secured the points for David Moyes' improving side, while the visitors finished with 10 men after Cesc Fabregas was shown a red card following a spat with Tim Cahill.
Everton started positively and Beattie almost got away from Gilberto before being body-checked. Mikel Arteta hit a stinging free-kick into the box, but couldn't find a blue shirt.
Arsenal could not find any sort of rhythm as Everton committed themselves to every challenge and the hosts began to reap the benefits, as Beattie found himself in space three times in as many minutes.
The former Southampton man is finding more consistency, but his first touch is still poor and that cost him on several occasions.
The Goodison faithful could sense an upset as Everton, orchestrated by Cahilll, Arteta and Leon Osman, began to dominate.
However, Arsenal should have taken the lead after 12 minutes. A Kerrea Gilbert cross evaded everyone but Freddie Ljungberg, who saw Nigel Martyn push his effort onto the post. The rebound fell to Fabregas but Tony Hibbert managed to block.
Two minutes later the goal Beattie had threatened came after Cahilll lofted the ball over the static Arsenal midfield. Beattie did well to shrug off the attention of Sol Campbell and Philippe Senderos and poked the ball past Jens Lehmann.
Arsenal were rattled and Lauren's disgraceful lunge on Arteta provoked a chorus of boos on 20 minutes, but referee Alan Wylie didn't think it deserving of even a booking.
Everton continued to pile on the pressure and the Gunners looked miles from the team that battered Middlesbrough 7-0 last weekend.
Beattie missed a golden opportunity on 21 minutes to double the lead. He intercepted a poor Fabregas back pass, but nonchalantly placed the ball wide of Lehmann's upright.
Matteo Ferrari, who had been enjoying his best game for the club, was substituted after 32 minutes for unlikely prodigal son Alan Stubbs, after the Italian looked to have tweaked a hamstring.
Beattie had the ball in the net again in first-half injury-time, only to be adjudged offside. Seconds later, he was yellow carded as he took his frustration out on Robert Pires.
Arsenal looked a shadow of their former selves as the half drew to a close. Shaken and bereft of ideas, Arsene Wenger must have been itching to get his bewildered team into the dressing room.
If truth be known, the Toffees could have gone in with a more comfortable cushion and Moyes would have been concerned at the interval.
Arsenal signalled their intent immediately in the second half, as Thierry Henry forced a corner in the first minute.
The high-tempo football that Everton used so successfully in the first half looked to have taken its toll as Arsenal started passing the ball more fluently and put the hosts on the back foot.
Henry and co were piling on the pressure but it was Everton who nearly added a surprise second, only for Campbell to intercept Osman's cross as Beattie waited to pounce.
Lauren was penalised for a foul on Arteta, which was followed by ironic cheers from the home crowd who felt Wylie had given them little all afternoon.
Pires forced a great save from Martyn with a blistering shot from outside the area, but Everton began to regain control in the closing stages.
Arsenal nearly conceded a bizarre own goal in the 80th minute. Campbell's lofted clearance fell to Beattie, who hit his shot at Lauren's legs and the ball evaded Lehmann, only for it to drift agonisingly past the post.
Pires was replaced by Abou Diaby as Wenger added some height to the Gunners' attack, before Moyes followed suit by introducing Duncan Ferguson for Arteta.
Everton nearly finished the game two minutes from time after a dogged Beattie run saw Cahill shoot straight at Lehman.
A late challenge from Cahill on Henry prompted a last-minute confrontation, which finished with the petulant Fabregas dismissed for grabbing the Australian by the throat. Cahill and Hibbert also collected yellow cards for the incident.
Overall Everton were well worth the win after showing a maturity often missing this season, whilst the Gunners were firing blanks.