Jack Spong’s hat-trick and a goal from Stefan Vukoje made it two wins from two games in the competition’s group stages, following last week’s 3-2 victory away at Leicester City.
The Seagulls worked their first opening when Sam Packham’s corner was met by Ed Turns, but his header flashed wide of the post.
Spong scored the first of his three goals with 30 minutes played when his superb free kick curled around the wall into the bottom left-hand corner to break the deadlock.
The midfielder found the net again five minutes later with a header from an in-swinging corner to double Albion’s lead.
The game was effectively killed off as a contest five minutes before the break when Spong tucked in a close-range finish at the end of a free-flowing move which involved a total of 19 passes from start to finish.
Albion then added a fourth goal nine minutes after the re-start, courtesy of Vukoje, who latched onto Marc Leonard’s through ball and provided a neat finish.
Substitute Odell Offiah nearly got in on the act himself, only to see his shot saved, while Vukoje saw another attempt go wide late on.
Mark Beard’s side will turn their attention back to their league campaign this Saturday when they host Aston Villa.
ALBION: Desbois; Turns, Cocoracchio, Clark-Eden, Furlong; Leonard (Offiah 65), Spong, Packham; Vukoje, Leahy (Dackers 73), Everitt (Collier 60).
SUBS NOT USED: Bull (GK), Tanimowo.