The north Londoners dictated the tempo and dominated possession but couldn't find the back of the net as summer signing Alexandre Lacazette moved to the bench and Olivier Giroud made his first league start of the season.
A disappointing midweek performance means the Gunners are now three league games without a win and drop to seventh in the table as a result of Tottenham Hotspur's 2-0 win over Brighton & Hove Albion.
Jack Wilshere made his first league start for the club in a little under two years, and Mark Mann-Bryans of the Press Association showed he wasn't the only unfamiliar face in Arsenal's XI:
England international Wilshere didn't look out of place in the lineup, however, and was linking up with the likes of Alexis Sanchez and Mesut Ozil nicely as the Gunners gained a foothold in the early phases of the clash.
Arsene Wenger's men were easily the oppressors of the first 15 minutes and barely allowed West Ham a touch in their third, while Layth Yousif of MailOnline hailed the performance of recently recalled goalkeeper Adrian:
The Spanish No. 1 was busy from the beginning, but West Ham's deep line meant his defence was able to crowd out numerous Arsenal chances, while Marko Arnautovic had a goal correctly ruled out for offside down the other end.
Despite the vast majority of chances falling Arsenal's way, however, former Manchester City and England defender Danny Mills felt the Hammers were hanging on as Alex Iwobi cannoned an attempt off the bottom of the woodwork:
West Ham might have been the submissive party heading in at the interval, but 0-0 was a fair scoreline considering the lack of finished product in attack for Arsenal, Giroud struggling to have the desired impact in a rare start.
But the home outfit gave a better account of themselves after the restart and began to show some more attacking verve, but the wetter the conditions got, the more it seemed to play into the hands of quick-passing Arsenal.
Iwobi made way for Danny Welbeck on the 70-minute mark while club-record signing Lacazette remained on the sidelines, despite the fact the drab display appeared to be begging for the Frenchman's input.
Lacazette came on for Sanchez with less than 10 minutes remaining but couldn't find the killer touch needed in front of Adrian's goal. Incredibly, it was West Ham who perked up in the dying exchanges and might have won all three points had substitute Javier Hernandez been able to capitalise on a Laurent Koscielny mistake:
Arsenal's troubling form away from home this season endures, and the Gunners are left to wonder where they might be this term had they managed to take opportunities such as this one, points they deserved.
Nevertheless, Moyes' promising start as Hammers hero continues, following up Saturday's win over Chelsea with an ugly point against the Gunners and a trip to Stoke City on Saturday next on the horizon.