After Ben White headed a Bowen corner into his own net to put West Ham in front inside the first 16 minutes, Kudus added a second for David Moyes's side with a brilliant sweeping shot across the face of goal five minutes after the break.
Bowen then put the Hammers in complete control when he rifled his seventh goal of the campaign and West Ham's third on the night beyond Aaron Ramsdale from the edge of the area, before Martin Odegaard netted a consolation strike for the Gunners with virtually the last kick of the game deep into stoppage time.
For the second successive year, West Ham have booked their place in the EFL Cup quarter-finals, where they will face Liverpool at Anfield in mid-December of this year's tournament.
Following a disappointing run of three consecutive defeats in all competitions over the last week, Bowen was pleased with West Ham's response against Arsenal and has insisted that they must «beat the best teams» if they wish to win silverware.
Discussing West Ham's performance against the Gunners, Bowen told Sky Sports: «It was massive. We knew what was at stake. We had the pleasure of winning a trophy in the summer and, when you're in so many cup competitions domestically and in Europe, you have a good chance of getting another trophy.
»We've spoke about how, if you want to win a trophy, you have to beat the best teams, and we've done that tonight.
«Of course, the week we've had wasn't our best but what is done is done. We had to face the opposition in front of us and I think you saw the hunger and drive
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