David Moyes' side are at the Emirates Stadium to take on the Gunners and found themselves with the ball in the back of the net inside the first 15 minutes of the game.
Following some good work from Jarrod Bowen down the left, the ball was squared across goal to Tomas Soucek who converted from close range.
However controversy struck when VAR intervened to check if the ball had gone out of play while in Bowen's possession - a decision that proved tricky to make.
The rules state that the whole ball has to be over the line for it to be deemed out of play, but despite consulting various camera angles, it a conclusive view couldn't be found due to Bowen's thigh blocking the view.
After lengthy deliberations, the decision was made to allow Soucek's goal, making it 1-0 to West Ham.
READ MORE ON ARSENAL
Xhaka details difference between Arsenal boss Arteta and Leverkusen manager Alonso
Darts sensation Littler leaves Arsenal duo starstruck and desperate for a photo
As you'd expect, Arsenal's supporters weren't impressed.
"Crazy decision," wrote one supporter.
Another said: "The agenda is real."
A third fan added: "That ball was definitely out!" with a fourth supporter stating: Once again VAR hates Arsenal."
Most read in Football
Arsenal 0-1 West Ham: Soucek puts Irons into lead at Emirates
Steve Cooper favourite for Crystal Palace job as Roy Hodgson faces uphill battle
Roberto Firmino faces uncertain Saudi future amid Premier League interest
Arsenal told to be ruthless and sell academy star to fund Premier League title bid
Arsenal had their opportunities to draw the game level before the break with Bukayo Saka having his header saved, before later seeing an effort hit the post.
West Ham doubled their lead early in the second half when former Gunner Konstantinos Mavropanos headed home to make it 2-0.
The Hammers then had a chance to make it 3-0 when Declan Rice gave away a penalty in the final minutes, only for David Raya to save Said Benahma's effort.
As a result Arsenal remain second in the Premier League table behind Liverpool, with West Ham moving up to sixth.