By the hour mark the Gunners found themselves 3-0 down, with Mohammed Kudus adding a second within five minute's of the restart and Bowen slotted home a third just shy of the hour mark.
Martin Odegaard pulled one back for the visitors deep into stoppage time, but it wasn't enough to avoid their elimination from the tournament.
Here are the player ratings of Wednesday's London derby.
Lukasz Fabianski - 6
Was barely tested by an indecisive Arsenal attack. Will be disappointed to have not kept a clean sheet, but could do little to stop Martin Odegaard's late consolation.
Vladimir Coufal - 7
It was a solid display by the Czech, who marked Leandro Trossard out of the match at times. He completed five clearances, two tackles and 1 interception across the 90 minutes. He also dealt well with Gabriel Martinelli when he came on.
A good performance by the former 'Gunners' player who no doubt felt like he had a point to prove against his former club. Dealt well with Eddie Nketiah - blocking a Reiss Nelson cut-back when at 0-0 which would have been a tap in for Nketiah. He won both of his ground duels and his one aerial duel.
Nayef Aguerd - 7
An assured performance from Aguerd, who marshalled his backline well. Was constantly organising and communicating with his defence.
Emerson Palmieri - 6.5
Possibly the least eye catching performance in the West Ham defence. He was caught out a few times in the first half by Reiss Nelson, who exploited space behind the Italian. Offered little going forward, an aspect of Emerson's game which is usually at a higher level.
Tomas Soucek - 7.5
A combative performance from Soucek saw him use his physical presence to great affect. Two tackles, one interception and four out of six aerial duels won. Impressive.
Edson Alvarez - 6.5
The least impressive of the two West Ham central midfielders on the night, although still a decent display. The Mexican was composed on the ball completing 90% of his passes (27/30). He did only win 2 out of his ten ground duels though, and looked slightly off the pace at times.
Mohammed Kudus - 7
An energetic performance from Kudus. Despite scoring a fantastic goal to double the Hammers lead, his work rate stood out above all on the night. Four tackles and one interception to go with his goal.
Lucas Paqueta - 8
Another quality performance from the Brazilian. The 26-year-old is really coming of age now in this West Ham side. He was always available to receive the ball in tight spaces as West Ham looked to bypass an Arsenal press. One big chance created, five tackles and 9/12 ground duels won.
Said Benrahma- 6
A passive performance from Benrahma, who struggled to get into the game.
Jarrod Bowen - 8
Despite playing out of position through the middle, it was a superb performance from Bowen. The England International got the ball rolling when his corner was headed in via a Ben White own goal. The 26-year-old got his goal on the hour, albeit somewhat fortuitously, with a deflected shot bamboozling Aaron Ramsdale.
James Ward-Prowse - N/A
Thilo Kehrer - N/A
Aaron Ramsdale - 4
After losing his place as first choice goalkeeper to David Raya, the oweness was on Ramsdale to impress. Unfortunately for him, it did not turn out that way. The 25-year-old could do little with the first two goals , but he made a mess of the third goal. His distribution was also not at the standard that Mikel Arteta demands.
Ben White - 5
It was not one of White's best games, with the own goal setting the tone for the match.
Jakub Kiwior - 6
A decent display from Kiwior - and one of the better in the Arsenal team.
Gabriel Magalhaes - 5
Not the greatest of performances from Gabriel. Could have done better in closing down the space on Mohammed Kudus for the second goal.
Oleksandr Zinchenko - 3
A very poor performance from Zinchenko. He was at fault for the second West Ham goal, losing his man Kudus in behind. It has been a tough couple of weeks for the 26-year-old, who is badly out of form.
Jorginho - 6
On a disappointing night for the 'Gunners' , Jorginho was probably the best of a bad bunch. There were a number of occasions where the Italian got team mates out of trouble in the first half, winning free-kicks regularly. He completed 93% of his passes, produces three key passes and won all four of his ground duels.
Fabio Vieira - 5.5
Vieira provided the assist for Martin Odegaard's late consolation , but it was a quite night from the 23-year-old who struggled to have any real impact on the match.
Kai Havertz - 4
A player visibly lacking confidence - it was another tough night for the German. He started the match reasonably brightly, winning a free-kick down the left hand side and doing well to convert a Reiss Nelson delivery on target. After that it was a match where you would be forgiven for not noticing that Havertz was playing.
Reiss Nelson - 5
Had a couple of dangerous runs at the West Ham defence in the first half, almost finding Nkeitah with a pull back after getting behind Emerson Palmieri being the standout moment. However, the 23-year-old did not offer enough to give Mikel Arteta any selection headaches ahead of Saturday's trip to Newcastle.
Eddie Nketiah - 4
A disappointing performance from Nketiah on the back of his hat-trick against Sheffield United on the weekend. He struggled to get into the match, and when he did, he was wasteful. All three of his shots were off target, including one big chance that was missed. In the absense of Gabriel Jesus, Arsenal are going to need more from Nketiah.
Leandro Trossard - 4
It seems that Trossard has a greater impact when coming off the bench in matches. He struggled to have impact on the match, having zero shots and creating zero chances across the 66 minutes he played.
West Ham offered much less down the left when he came on with 57 minutes played.
Declan Rice - 5
Bukayo Saka - N/A
Gabriel Martinelli - N/A
Martin Odegaard - N/A
A superb finish to grab Arsenal a late consolation, but not on long enough for a rating.