Arsenal shot out of the blocks with Theo Walcott again showing manager Arsene Wenger why he deserves a new contract by firing the Gooners ahead in the first minute.
Everton settled and the game became a more balanced affair before Marouane Fellaini, Everton's top goal scorer so far this season, fired in a low drive from outside the penalty area just before the half-hour mark.
The game ebbed and flowed with Everton creating the better chances: Nikica Jelavic smashed his shot over the bar after some great control, Steven Naismith missed a great chance in the area and a header from Sylvain Distin was well saved by Arsenal goalkeeper Wojciech Szczesny.
Arsenal looked a little toothless in all honesty, lacking that presence in the final third that now resides in Manchester.
Everton, who have only won one in their last eight games, could really use a win to kick on from their great start to the season and with Manchester City their next game up, the Blues could have done with three points.
The Blues do lie at sixth in the Premier League table though, and while the Arsenal game did not deliver in terms of points, the game did show some signs of life that Everton will be encouraged by.
Everton's defensive performances have been rather poor of late, particularly in the second half of matches.
The Arsenal game offered up a different prospect with Theo Walcott's first-minute goal. From there, Everton's defense could only get better.
Phil Jagielka was the star performer, producing a phenomenal last-ditch tackle on Gervinho in the final minutes of the game sparing Everton another late goal.
Jagielka still launches the ball forward a little bit too much, but when he is aiming for and connecting with Marouane Fellaini it is difficult to complain.
His central partner Slyvain Distin played well. He was strong in the air and in the tackle and in dealing with the aerial threat of Olivier Giroud well.
Leighton Baines is Leighton Baines, another strong performance from the best left-back in the Premier League both on attack and defense.
And Tony Hibbert tries really hard!
Finally, midfielder Darron Gibson made his return from a thigh injury in the 1-1 draw with Arsenal.
While Gibson did look rusty in his first game since September 1, the Irishman brought a calm presence to the Everton midfield that has been greatly missed.
It was no coincidence that Everton had a much better defensive performance while Gibson was on the field.
Gibson removes the pressure from the back four by breaking up much of the opposition play before it can develop, with Arsenal's ability to keep the ball, Gibson had a lot of work to do, but he did manage to spoil several Arsenal attacks.
While his fitness is obviously lacking, for a first time back after a lengthy layoff, Gibson looked solid, and he can only improve in the coming games.
Last season, Nikica Jelavic had that Midas touch, but his form has dipped of late.
Jelavic was poor against Norwich and was better against Arsenal, getting into good positions and linking up well with Marouane Fellaini, but you can see he is lacking the confidence that is so important for a striker.
The Croatian international struggled to get into the game and was often isolated on his own up front. He made some silly mistakes by straying offside and denying Leighton Baines a glorious chance to put Everton ahead.
Jelavic had a fantastic chance that he ballooned over the bar after turning Arsenal centre-half Per Mertesacker on the edge of the penalty area mid-way through the first half.
You couldn't help think that Jelavic of last season would have collected the ball from his brilliant turn and stroked the ball past the on-rushing Arsenal goalkeeper Wojciech Szczesny.
Jelavic is without a goal since the Sunderland game on November 10, so it isn't as if he is in the midst of a Fernando Torres-esque funk, but a goal sooner rather than later would be a great relief for Evertonians everywhere.
One half of Everton's fantastic left side, midfielder Steven Pienaar, has been lackluster in the last couple of weeks.
Against Arsenal, Pienaar was nearly back to his best, linking up well with Leighton Baines throughout the first half and assisting Marouane Fellaini's equaliser.
While the South African international tired through the second half, he still caused Bacary Sagna problems going forward as he crept behind the French right-back repeatedly but couldn't do more with his extra space.
Evertonians know the importance of Pienaar and his on-field relationship with Leighton Baines and will be delighted with these signs of life from the influential midfielder.
Hopefully Pienaar can build on this strong performance in the coming weeks as they look to push through this mid-season blip and return to winning ways.
Scottish international Steven Naismith had an awful game against Arsenal on Wednesday night.
Paired on an ineffective right side with Tony Hibbert, Naismith lost possession all too easily throughout the night and missed a good chance to put Everton ahead before being replaced after an hour.
Naismith's performance highlighted the affect that Kevin Mirallas has had on the Everton first team.
With Mirallas in the lineup, Everton have a more balanced attack but without him, the right side of the field looks toothless.
While Naismith has done well to net three goals so far this campaign, Mirallas has been the star of Moyes summer signings and he is sorely missed.
Naismith can be a successful squad player for Everton, but a starter he is not.
A couple of seasons ago, Evertonians would have bitten your hand off for a point against Arsenal, but not anymore.
Filing out of Goodison Park on Wednesday night, the grumbles were audible as Toffee fans thought they deserved more than their solitary point.
Arsenal looked good in possession, but lacked a cutting edge while Everton created the better chances but just couldn't finish the game off; a worrying trend.
While Arsenal had most of the money and big-name talent on the field, Everton produced a well-rounded performance and man of the match Marouane Fellaini was, yet again, masterful.
It is only in games against the likes of Arsenal, Tottenham and Liverpool, the development of Everton Football Club becomes evident. They have what it takes to battle with the best sides in England outside of Manchester.
Disappointing results against Reading and Norwich in back-to-back games masked strong performances. Since their fantastic start, Everton have slowed somewhat.
However, the Toffees still show great development as they continue to push for a Champions League place this season.
A question for another day: Does this reversal of fortune speak more of the rise of Everton, or the demise of Arsenal?