Arsenal were quick out of the blocks, with Theo Walcott enhancing his striking reputation with a goal after less than a minute, but a fine finish from Marouane Fellaini levelled the game up.
The second half was a more scrappy affair, with both sides creating chances without any serious chance of a winner.
This was billed as a battle between two clubs aiming for a top-four finish, but in truth both sides had worries coming into the match. Everton had won just one of their last seven Premier League games, whilst recent draws for Arsenal against Fulham and Aston Villa had led to worries that the North London club would again fall short of hopes and expectations.
Arsenal had not lost to the Goodison club in ten outings, winning both fixtures last season without conceding, and they started frighteningly quickly. Less than a minute had been played when Walcott's finish clipped Tony Hibbert before looping into the top corner, leaving Tim Howard stranded.
Everton responded by quickly getting a foothold in the game, with Fellaini heading straight at Wojciech Szczesny and then having another header patted off the line by the goalkeeper from a Leighton Baines corner.
Kieran Gibbs, an early substitute for the injured Laurent Koscielny, was booked as Everton searched for an equaliser.
Thomas Vermaelen tested Howard with a skidding free kick, but it wasn't long before Everton were level. Arsenal twice gave the ball away cheaply in defence, but it was a beautiful low curled finish from Fellaini that left Szczesny helpless.
Everton started brightly in the second half, and Steven Pienaar shot wide of Szczesny's near post as Fellaini began to have more influence in the game.
The South African midfielder then forced a smart save from the keeper from a tight angle, as the game became slightly scrappy. From the resultant corner, Szczesny was forced to tip the ball away from a Sylvain Distin header.
Arsenal finally clicked to into gear after 70 minutes, and Olivier Giroud was unlucky not to score after a header from a fabulous Walcott flashed just wide. Soon after, Aaron Ramsey fired over.
Thomas Hitzlsperger came on for Everton and immediately stung the fingers of Szczesny, but in truth the second half failed to live up to the standard set during the first period.
In the end both sides seemingly settled for a point, though whether such a tactic would please fans is up to some debate.