It was a fairly open start to the game with West Ham controlling the possession early on, however both sides had a handful of chances in the opening exchanges.
Despite spells of control, Arsenal never looked to really get going in the first half and they fell to an early own goal, following a West Ham corner.
With no Video Assistant Referee (VAR) in use, appeals for a foul in the build-up went unheard.
West Ham took complete control in the second half, with both Mohammed Kudus and Jarrod Bowen adding their name to the scoresheet as the hosts etched out a three-goal lead.
A late consolation goal did little to help the Gunners as West Ham saw out the game, earning a comfortable 3-1 win and securing their place in the draw for the quarter-finals.
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Story of the Match
David Moyes named a strong West Ham side, with five changes from the side who fell to a 1-0 defeat at home to Everton at the weekend.
This included a start for the highly rated Kudus, just his sixth since arriving from Ajax in the summer.
Arsenal also put forward a strong side, despite Mikel Arteta making six changes from the side who demolished Sheffield United 5-0 last Saturday.
In what will be a source of real concern though, Emile Smith-Rowe was absent with a knee injury - the extent of which is currently unknown.
The Hammers started the game on the front foot and were trying to test the Arsenal defence right from the off, though they were unable to make their early pressure count, and the Gunners soon found their feet in the game and began to take control.
Just eight minutes into the game the visitors had a great chance to take an early lead via a Reiss Nelson free-kick.
The delivery found Kai Havertz in the box, but his header was tipped over the bar by Łukasz Fabiański.
From there Arsenal were in total control and creating chance after chance - though they were unable to find a way to break the deadlock at the London Stadium.
After a fruitless period of sustained pressure from Arteta's side, there felt to be something of a shift in momentum which saw the hosts enjoying much more of the ball.
The Gunners would quickly come to regret not taking their early chances as West Ham won a corner in the 16th minute.
Bowen delivered the ball towards the near post, where Ben White ran onto it and sent it into his own net - giving the hosts an early lead.
Arsenal players appealed ferociously for a foul after Aaron Ramsdale's shirt was seemingly pulled by Tomáš Souček, but with no VAR in use for this game, the goal stood unchallenged.
Despite going a goal behind, the Gunners reasserted their control of the game and created numerous chances in search of an equaliser - but to no avail.
A great chance fell to Eddie Nkeitah in the box, but last weekend's hat-trick hero was off-balanced and saw his shot blaze over the bar, which perhaps epitomised the visitors' evening.
Arsenal were still in control of the game but looked vulnerable on the counter, though neither side were able to find any meaningful chances.
The hosts spent the last minutes of the half sitting deep and at times had six or seven players in their own box - making it incredibly difficult for Arsenal to carve any opportunities.
West Ham, clearly not happy with just a 1-0 lead, came racing out of the blocks in the second half and quickly took control of the game once more.
It was not long, after some fairly constant pressure from the Hammers, that they found a way through again.
A long ball was played over the top to Kudus, who then turned beyond Oleksandr Zinchenko before placing it past Aaron Ramsdale in spectacular fashion.
Even after doubling their lead, Moyes' side looked to attack straight from kick-off in a bid to see the game beyond doubt.
There was a brief period where the hosts looked to have eased off slightly, which allowed a glimmer of hope for the chasing visitors - though they were unable to create anything meaningful.
Arsenal's fate was sealed a handful of minutes later as Bowen blasted an effort from range straight at Ramsdale, who was powerless to stop it from creeping into the net over his head.
Having made a couple of substitutes just before the third goal, Arteta once again turned to his bench as the Spaniard looked to change the game.
Both Bukayo Saka and Gabriel Martinelli came on to the bemusement of some, who did not see the point in risking a needless injury when already trailing 3-0.
While you would be forgiven for expecting West Ham to sit back after putting the game beyond doubt, rest was not on their agenda as they still pilled pressure on the Arsenal defence, looking to prolong their suffering.
The visitors looked to be improving slightly as the game went on, but were unable to generate any clear chances, and never truly threatened Fabiański's goal.
As floods of Arsenal fans left the ground early, the game looked to be petering out in what was a frankly dull conclusion to the affair - not that the Hammers fans cared.
There was to be one more twist to the tale though as some good play deep into injury time saw Martin Ødegaard with a chance to pull one back, which he did in clinical fashion to deny the hosts of a clean sheet.
It would count for nothing in the end though, as the referee brought proceedings to an end soon after, ensuring a comfortable home win for Moyes and his team.
The three-goal deficit proved too great for the Gunners to overturn as they succumbed to a humbling 3-1 loss in East London - and the Hammers booked their place in the quarterfinals of the Carabao Cup.
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Player of the Match - Mohammed Kudus
Several players stood out for the hosts, but Kudus felt like he just about edged it to claim our player of the match.
The Ghanaian took his goal perfectly - from beating Zinchenko to an excellent finish.
It was not just his goal though, with his general play also a joy to behold - unless you happen to be an Arsenal fan, of course.
His passing boasted terrific accuracy and the 23-year-old also dropped back at times to help his side in a defensive capacity.
It is clear to see why West Ham were so keen to secure the services of Kudus in the summer and as he continues to settle into his new side and play more minutes, his output will only increase.
