Arsenal suffered a first home defeat of the Premier League campaign after going down 2-0 to London rivals West Ham United on Thursday night.
Leandro Trossard was recalled to the Gunners' line-up after the 1-1 draw with Liverpool over the weekend, as Kai Havertz was suspended for an accumulation of yellow cards.
The Hammers made the perfect start after Tomas Soucek sent a first-time finish beyond David Raya after Jarrod Bowen managed to keep the ball in by a small in margin in the build.
Mikel Arteta's charges remained in control despite going behind but they were finding it tough to break a stubborn Hammers defence, who were happy to soak up the pressure.
The Gunners went agonisingly close to find the leveller a few minutes before the interval as Martin Odegaard's intricate pass sent Bukayo Saka through on goal, but the England international's was kept out by the post.
Arsenal were made to rue that miss as the Hammers doubled their lead ten minutes after the halftime break, with Konstantinos Mavropanos nodding home from a corner against his former side.
The hosts went close to pulling one back with 25 minutes when Gabriel Jesus got on the end of Saka's in-swinging cross, but saw his header saved by goalkeeper Alphonse Areola.
West Ham were afforded the chance to pile more misery on Arsenal in time added on after being awarded a penalty for Rice's foul, but Said Benrahma was denied by a good save from Raya.
Two goals were enough to hand Moyes' side maximum points on the day while also denying the Gunners a chance to move top of the Premier League table.
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