Robin van Persie's curling free-kick claimed a point for Arsenal as Everton hung on to frustrate the hosts.
Cahill fires Everton into an 11th-minute lead
Tim Cahill blasted the Toffees in front after 11 minutes when some woeful Arsenal marking allowed the Australian to volley home Mikel Arteta's corner.
Everton looked set to become the first team to beat Arsenal at the Emirates after a resolute defensive display.
But the defenders could only watch as van Persie bent in his curling set-piece, despite Tim Howard's touch.
Arsenal were looking for their six successive victory and quickly pegged back the visitors when Johan Djourou burst from defence and was bundled over inside the box by Phil Neville.
Referee Mike Riley waved away appeals for a penalty after the Swiss defender had exchanged a neat one-two with Thierry Henry.
But after 11 minutes the hosts fell behind after some appalling Arsenal defending from a corner.
Arteta's whipped set-piece found the unmarked Cahill who strolled through a cluster of red shirts and rifled his close-range shot into the roof of the net.
The goal forced Arsenal to increase the tempo and Everton spent the majority of the first period camped inside their own half.
But for all the Gunners' neat build-up and intricacy around the Everton box, a tame Fabregas effort and Henry's drilled shot from 25 yards were the only occasions in which Howard was forced into action.
And shortly before the break Arsene Wenger's side suffered another defensive setback as Justin Hoyte hobbled off injured.
Robin van Persie celebrates Arsenal's equaliser
Despite showing precious little going forward, the Toffees disrupted Arsenal's rhythm and stubbornly contained the Gunners midfield by packing five into the middle of the park.
Arsenal flew out of the blocks after the break as Henry's cushioned header brought a fine full-stretch save from Howard while Tomas Rosicky curled an effort on to the roof of the net.
Desperately seeking an equaliser, Wenger threw on Theo Walcott in place of Djourou.
But it was from a set-piece that Arsenal responded as Howard failed to keep out Van Persie's fierce free-kick from 25 yards. The American got a firm palm to the ball but could only tip the effort into his own net.
Arsenal bombarded the Everton goal in the last 15 minutes but the Toffee's defence held firm under the intense pressure.
David Moyes was sent to the stands for contesting the amount of added time at the end of the match, but seconds later referee Riley blew for time to give the Scot's side a hard-fought point.
Arsenal manager Arsene Wenger:
"It was very frustrating, but we shouldn't have conceded the goal in the way we did.
"Everton deserve the credit for the way the defended. They were very intelligent and once they went 1-0 up they never came out. But I was not pleased with the way the gained time from goal kicks and free kicks.
"When you play like we play we have the ability to open up teams and punish them, but unfortunately we weren't able to do that today."
Everton manager David Moyes:
"The lads showed great character and there is a bug doing the rounds and I may have to give them a few days off to recover.
"All the lads who have played with injuries and illness need a pat on the back for their performances.
"It's great for the lads to come here and get a result, especially the way they played against Reading last week."
Arsenal: Lehmann, Hoyte (Flamini 39), Toure, Djourou (Walcott 67), Gallas, Silva, Hleb (Aliadiere 79), Rosicky, Fabregas, Van Persie, Henry.
Subs Not Used: Almunia, Senderos.
Booked: Gallas, Fabregas.
Goals: Van Persie 71.
Everton: Howard, Neville, Stubbs, Yobo, Lescott, Davies, Cahill, Carsley, Osman, Arteta, Johnson.
Subs Not Used: Turner, Hughes, Beattie, McFadden, Anichebe.
Booked: Arteta, Osman, Cahill.
Goals: Cahill 11.
Ref: M Riley (W Yorkshire).