Town claimed a crucial three points from a game of few chances, which saw Charlie Austin rediscover his goal scoring touch at The Withdean.
Brighton started the match the stronger, and dominated possession early on, getting wingers Lua Lua and Bennett on the ball whenever possible.
Shortly after the 10 minutes mark, David Lucas collected the ball and put it straight out of play clutching his thigh, and was replaced immediately by Phil Smith.
However this seemed to galvanise Town, who began to look more assured in possession and swung numerous crosses into Peter Brezovan's box.
The game drifted towards the half hour mark without incident, until both sides had chances to break the deadlock.
Glenn Murray's back post header was cleared off the line by Greer, and then on the subsequent counter attack, Charlie Austin was inches away from poking J-P McGovern's cross over the line from close range.
Town were then further disrupted with the withdrawal of the injured Vincent Pericard, and the half ended as it had started: with the hosts looking dangerous from the wings and the most likely team to score.
However Town had the best chance shortly before the sides went into the break level, with Scott Cuthbert's header being cleared off the line, but it was all square at half time.
Danny Wilson introduced Craig Easton in place of Danny Ward at half time, and moved to match the hosts' 4-5-1 formation.
Town looked effective in the new set up, with Marshall, Ferry and McGovern all looking to break forward to support Austin from midfield, with Douglas and Easton in the holding rolls.
The lone striker could have put Town in front when he latched onto the loose ball after Adam El-Abd had missed his clearance, but the striker's shot rolled just wide of Brezovan's post.
The similar systems then began to cancel each other out, until both sides had efforts cleared off the line in the space of two minutes - first Greer's header was well saved by Brezovan, and then Alan Sheehan was on hand to deny Elliott Bennett's weak goalward poke with Smith beaten.
Town were then rewarded for their industrious performance with a goal in the 71st through Charlie Austin. Good work on the right from the impressive Mark Marshall resulted in a cross which McGovern controlled well, before laying it off to Austin who made no mistake from 10 yards; slotting it past Brezovan for his 14th of the season.
Albion then brought on Nicky Forster and moved to two up front in an effort to claw back the equaliser.
The pressure then inevitably increased on the Town goal, as the hosts threw caution to the wind and won corner after corner, but the visitors' rearguard held firm as the game moved into its final five minutes.
And despite the hosts' initially impressive reaction to going behind, yet more colossal defending from Scott Cuthbert and Gordon Greer saw Town close the game out, and clinch what could prove to be a crucial three points in the League One promotion race.