© PA Photos
Visitors Everton had the first chance of the match in the sixth minute when Seamus Coleman's through-ball made its way to Steven Pienaar, but the South African could only balloon over the crossbar.
As the first-half drew to a close, both sides had chances to go ahead. First Ross Barkley turned cleverly in the middle and fed Victor Anichebe. The striker was challenged when shooting but the ricochet almost squeezed under the sprawling Wojciech Szczesny.
Barkley was earning a rare start for Everton and he almost broke the deadlock after 64 minutes when he shifted the ball onto his right foot outside the area and fizzed a curling effort inches wide of the top corner.
Arsenal's best chance of the match came with 13 minutes left when they broke quickly from an Everton attack. Lukas Podolski freed Cazorla and he waited for Alex Oxlade-Chamberlain's run on the overlap, with the Englishman's cross well defended by Coleman with Giroud ready to tap in.
Giroud did manage to get a shot away two minutes later when Oxlade-Chamberlain found his French teammate. Giroud sidestepped Phil Jagielka but rifled over from an acute angle.
A point leaves Arsenal two points clear of both Chelsea and Spurs in fourth and fifth respectively, while Everton are a further two back in sixth.