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Mikel Arteta's Gunners were top of the tree at Christmas for a second successive year but trail leaders Liverpool by two points at the halfway point of the season.
Arsenal, last year's runners-up, dominated possession but lacked a cutting edge against the disciplined visitors, for whom Tomas Soucek and Konstantinos Mavropanos scored the goals.
Arsenal surged forward in waves and West Ham goalkeeper Alphonse Areola made a reaction save from a Bukayo Saka header on the half-hour. The England winger hit the post from a tight angle as the clock ticked down towards half-time but Arsenal trailed at the break despite enjoying nearly three-quarters of possession.
The Gunners came out determined to find a response but instead they found thelves 2-0 down when Mavropanos's bullet header cannoned in off the crossbar from James Ward-Prowse's corner.
