Having ended a winless run last week with a 4-1 victory over the Bees, Simon Rusk's side made it a win double against their north London opponents.
Two goals in five first-half minutes were enough to give Albion all three points, with Deen opening the scoring just past the half hour mark.
The forward was excellently picked out by Jack Rowhurst before firing home from an acute angle, and the attacker doubled his and Albion’s tally with an excellent strike into the top corner after a well worked set-piece.
Albion didn’t trouble the Barnet goal frequently in the second half as they found themselves under heavy pressure which they withstood determinedly.
But the hosts did set-up a tense finale with a magnificent free-kick to half the deficit on 88 minutes, but it came too late for the Bees as Rusk's side held out for all three points.
He told seagulls.co.uk, “It was not one of our better performances but credit to the boys for the win. It was the second time we'd faced them in a week and they seemed to work harder against us this time around and put us under a lot more pressure. But overall we played the better football.
“They bombarded us in the second half but it was determined performance and a case of winning ugly. At the end of the day it was not a good performance and the players agreed but we have played better and not come away with anything this season.
“I wouldn’t call it an up-turn in form; it has just been better results, and we have deserved more from other games, but there are ups and downs in football. We want to win games and we did that away from home with a young side which is pleasing.”
Albion (4-3-3) Walton (GK), Courtney (Collar 55), Rea, Cooper, Gray; Peake, Wilshire (Harris 45), Benham; Rowhurst, Levy (Muitt 75), Deen. Subs not used: Colquhoun, Lall.