The full-back picked out Dean Windass who finished in clinical fashion from 12 yards for his sixth of the season.
Brighton pulled level on 14 minutes, leading scorer Bobby Zamora in space on the left flank dragged the ball past Robert Page as he picked out the unmarked Richard Carpenter who stabbed the ball in from 12 yards with keeper Paddy Kenny stranded.
Paul Watson beat the wall with a free-kick minutes later, the United keeper scooping up the ball on the line. Paul Brooker miscued and Simon Rodger fired wide as the First Division strugglers looked for a second.
United's £5million-rated midfielder Brown snatched the lead with a spectacular free-kick in the 34th minute after he had been brought down by Brighton skipper Danny Cullip.
The ex-Manchester City man fooled Dave Beasant, tucking the ball into the bottom left-hand corner with the veteran keeper expecting him to loop it over the wall.
Windass squandered an opportunity minutes after the restart heading over from a Michael Tonge corner before Ivar Ingimarsson went close, his fierce header being snapped up on the line by Kenny.
Steve Kabba should have killed off Brighton in the 56th minute as he beat his marker to Brown's curling free-kick but headed over the top from six yards.
Former Sheffield Wednesday midfielder Owen Morrison almost grabbed a spectacular goal minutes after replacing the ineffective Peter Ndlovu, his 40-yard run into the area ending with a stinging shot being tipped over the top by Beasant.
Brighton sub Graham Barrett was foiled by Kenny and had the United back four in a panic minutes from time, Page finally clearing as the Seagulls desperately looked for an equaliser.