They scored four times in the second half and eventually more than matched Everton’s physical style.

In the past Arsene Wenger’s sides have suffered against the combative Merseysiders and been bullied out of matches, but after hitting back from a goal down at the break, the Gunners showed their own hard edge.

Tim Cahill had stabbed Everton into a deserved lead at the break, but Everton were overcome in spectacular fashion.

Brazilian forward Eduardo struck twice to take Arsenal into the lead, his first goals in the Premier League although he now has nine in 10 games for the Gunners.

Both teams had men sent off. Arsenal lost striker Nicklas Bendtner, while Everton’s Mikel Arteta was dismissed for a flaying arm into the face of his fellow Spaniard and friend Cesc Fabregas.

Arsenal rubbed it in with goals from substitutes Emmanuel Adebayor and Tomas Rosicky as Everton fell to their first home defeat since mid-October by Liverpool.

Everton made one change from the side that beat Bolton on Boxing Day. Thomas Gravesen was out with a knee injury, allowing Tony Hibbert into the side at right-back with Phil Neville switching to midfield.

Arsenal, who had lost this fixture four times in the last seven seasons, left Rosicky and Adebayor on the bench and rested Emmanuel Eboue.

Abou Diaby and Eduardo came in, along with Bendtner who made his first Premier League start.

Arsenal were swiftly into their quick-passing game, no doubt boosted by news of Manchester United’s 2-1 defeat at West Ham.

But it was no surprise when Everton took the lead on 19 minutes.

Ayegbeni Yakubu forced a corner from Kolo Toure with determined running, and when Mikel Arteta swung the flag-kick into the box Arsenal failed the deal with it.

Tim Cahill, with his flying boot, and Yakubu with his head, both hurled themselves at the ball and it looked as if the Nigerian got the final touch, but TV reruns showed that Cahill’s studs got the last connection.

Mathieu Flamini was involved in a pushing match with Cahill and Bendtner was booked for dissent on 24 minutes.

Yakubu pulled an 18-yard shot wide after a neat Steven Pienaar flick, and Neville fired just over after Yakubu, Cahill and Hibbert had created the chance on the edge of the box.

Arsenal needed to get themselves back into the game quickly, and they did just that a minute after the break with the sort of approach that Wenger often criticises.

Gael Clichy launched a 60-yard long ball from deep in his half and it flew straight to Eduardo racing into the box.

For a second it looked as if he had controlled the ball with his arm, but the connection was with the shoulder and he was able to turn and calmly strike the ball past Tim Howard.

Yakubu headed wide from a great position after Joleon Lescott’s right-wing cross, but on 57 minutes Eduardo scored again.

Another long ball, again a fleeting suggestion of a hand involved, but the Brazilian coolly beat Phil Jagielka, who slipped trying to turn. The Brazilian eased his shot just inside the post and Arsenal were ahead.

Everton sent on Andrew Johnson for Hibbert, and Arsenal replaced Eduardo with Adebayor, but between these substitutions the Gunners found themselves reduced to 10 men.

Bendtner, already booked, went through on Johnson’s ankle on 74 minutes and received a second yellow from referee Martin Atkinson, although it could easily have been a straight red.

But four minutes later Arsenal got their third, another huge punt down field and this time a calamity between Joseph Yobo and Howard.

Manuel Almunia launched his goal-kick, it bounced once inside Everton’s half with Yobo waiting for Howard to deal with it as it approached the area.

Adebayor stuck out a long leg and kicked the ball at Howard, the rebound dropping for the substitute to run into an empty net.

Any plan for a last-ditch bombardment was over now, and on 84 minutes Everton also found themselves down to 10 ten men.

Arteta’s arm caught Fabregas in the face and the Spaniard hurled himself to the ground, Atkinson showing Arteta a straight red card.

Fabregas was booked a minute later for felling Pienaar, and Flamini also saw yellow for failing to retreat from the free-kick. Fabregas was soon to be replaced by Rosicky.

And it was the Czech who fired home the fourth in injury time from the edge of the box.