The Gunners had won four league games in succession to move above Tottenham and Chelsea in the race for Champions League qualification.
However, despite plenty of endeavour, Arsene Wenger's men were unable to breakdown a determined Everton side, who utilised all their physical qualities if not collecting the win they probably needed to harbour any real hopes of getting into the top four.
Arsenal's best chances fell to Olivier Giroud but the France striker failed to test Tim Howard and the hosts had to be content with a point which sees them move two clear of their London rivals below them but having played more matches.
It was a lively start by Everton and after six minutes, Steven Pienaar was played into the right side of the Arsenal penalty area by Seamus Coleman but lifted his shot over both goalkeeper Wojciech Szczesny and also the crossbar.
Chances were few and far between, as Victor Anichebe squirmed a shot away in the Arsenal six-yard box, which hit a defender and then Szczesny's legs before being gathered.
After 41 minutes, Giroud should have put Arsenal ahead when Aaron Ramsey got away down the right and swept the ball back through the penalty area, where the French striker arrived at pace ahead of goalkeeper Howard - but stabbed the ball wide.
Santi Cazorla tested Howard following the restart with a rasping half-volley as Arsenal looked to break down the stubborn visitors.
Everton, though, refused to lie down and were awarded a free-kick just outside the penalty arc in a central position when former Toffees midfielder Mikel Arteta tripped Pienaar - but Leighton Baines fired it into the wall.
Ross Barkley was inches away from slotting Everton ahead with a curling effort after side-stepping a couple of challenges on the edge of the Arsenal penalty area. Giroud then showed good footwork to fashion a shooting chance from a tight angle but blasted over.
- Sports & Recreation
- Olivier Giroud
- Tim Howard