The Gunners had beaten Bayern Munich on Tuesday night to kickstart their Champions League campaign, and were out to take advantage of leaders Manchester City not playing until Sunday's derby with United at Old Trafford.
Quickfire first-half goals from Olivier Giroud and Laurent Koscielny in the space of two minutes look to have set the Gunners up for a comfortable evening.
However, Everton were back in the contest just before half-time when Ross Barkley's effort deflected in off Arsenal defender Gabriel.
After Giroud had hit the crossbar, the visitors, who lost captain Phil Jagielka to what could be a serious knee injury, rallied, with Romelu Lukaku sending a header onto the top of the woodwork.
Gerard Deulofeu saw a late effort beaten away by a great block from goalkeeper Petr Cech, before Arsenal playmaker Mesut Ozil hit the outside of the post and then Toffees' midfielder Gareth Barry was shown a second yellow card in stoppage time.
While Wenger accepts there is little to read into the league table just yet, things are now starting to come together for the Gunners, who had Theo Walcott kept in reserve on the bench.
"It is a perfect week and it is not easy to have that," said the Arsenal boss.
"I believe that we will keep that solidarity, that desire to do well and I think we are well focused to do well and together we have improved on that front and we know that when we have the ball we can create goal chances.
"We went to Watford and won 3-0 and beat Bayern Munich 2-0 and beat Everton tonight in one week, it has been a fantastic week
It is not easy.
"The only negatives is that we lost some players through in jury during the week, but I will have to rest some players Tuesday night against Sheffield (Wednesday in the Capital One Cup) as I think for some players I think it will be one game too many for them."
Wenger admitted he did not expect Arsenal to be at the head of the table at this stage following their poor start
"I thought after 10 games, no, honestly
I thought it would take much longer because Manchester City started with five wins, so it was difficult to envisage that we would come back but we had no choice," said Wenger
"But we are there, that shows we have made some ground up, so let's keep our togetherness and fight for the future games, that is all we can do
"It is very early in the season but we are happy to be where we are."
Everton boss Roberto Martinez, whose side were beaten 3-0 by Manchester United last weekend, believes the Gunners will have a big part to play in this season's title race.
"Arsenal is in very good form and if you allow them to do what they are good at they will stand out in the competition, but I don't think it is going to be decided yet in October," he said.
"The season is very long, it is very demanding
We have got very good teams and probably it is going to go down to the very last game."
England defender Jagielka, meanwhile, will undergo tests to determine the extent of the damage
"It will take probably 48 hours to find out the damage, but it's not good," said Martinez
"We do not know at this point the extent but the structure we know is going to be damaged
To lose Jagielka in such a stupid challenge, an unnecessary challenge is frustrating."
Source : PA
Source: PA