Mark Beard's men reached the last 16 with a 2-1 win over Derby County at Pride Park on Wednesday night thanks to goals from Jack Leahy and Teddy Jenks.
The Seagulls were also 3-2 winners over Leicester City in round three of the competition at The People's Pension Stadium back in December.
A brace from Stefan Vukoje and a decisive winner from Lorent Tolaj were enough to seal progression that evening before the win against the Rams earlier this week, and now the Gunners lie in wait in round five.
A date and venue for the tie will be confirmed in due course.